prime number problem solving year 5

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Year 5 - Number

Standard 5.NS.1.3 - Practice identifying prime and composite numbers.

Included Skills:

Number - multiplication and division • Pupils should be taught to: - identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers - know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers - establish whether a number up to 100 is prime and recall prime numbers up to 19 - multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers - multiply and divide numbers mentally drawing upon known facts - divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context - multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 - recognise and use square numbers and cube numbers, and the notation for squared (�) and cubed (�) - solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes - solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign - solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

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Prime numbers

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What is a Prime Number?

Welcome to our What is a Prime Number? page. Hopefully all (or nearly all) your questions about prime numbers will be answered here!

There are also links to our prime number charts page and our prime number calculator.

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Here are the instructions how to enable JavaScript in your web browser .

What is a prime number?

• A prime number is a positive whole number that is only divisible by itself and 1 .
• Prime numbers must be greater than one.

Another way of saying this is that the only factors of a prime number are 1 and the number itself.

What is a composite number?

• A composite number is a positive whole number that can be made by multiplying two smaller positive whole numbers.
• Every positive whole number, apart from 1, is either prime or composite, and cannot be both!

So a number which is prime cannot be composite, and a number which is composite cannot be prime!.

The First 5 Prime Numbers

If you want to find out what the first 5 prime numbers are and why, then take a look at our First 5 Prime Numbers page.

• First 5 Prime Numbers
• Prime Number Calculators

Our prime number calculator will help you to find all the factors of any given number and tell you whether or not the number you are looking at is prime or not.

The calculator will also show you your number as a product of primes.

Examples of primes

11 is prime because its only factors are 1 and 11.

17 is prime because its only factors are 1 and 17.

53 is prime because its only factors are 1 and 53.

15 is NOT prime because it has 4 factors: 1, 3, 5 and 15. So 15 is composite .

28 is NOT prime because it has 6 factors: 1, 2, 4, 7, 14 and 28. So 28 is composite .

• Prime Number Charts

On our Prime Number Charts page, we have many printable lists of prime numbers.

You can find the first 100 prime numbers, or print out a list of all prime numbers below 10,000.

We also have a prime number calculator which will find all the primes in a range that you set, and also a prime number tester which gives all the factors of a number, and tells you whether it is prime or not.

• Prime Numbers Lists

Is one a prime number?

The simple answer to this question is no .

Prime numbers have many different and interesting properties, which they would not have if the number one was prime.

Therefore, the number 1 was excluded from the set of prime numbers.

So the first prime number is 2.

Can prime numbers be negative?

The answer to this question is no .

All prime numbers belong to the set of natural numbers or positive integers.

Can prime numbers have a decimal or fraction value?

The answer to this question is again no .

They cannot be decimals or fractions.

Are some prime numbers even?

The answer to this question is yes .

However, there is only one even prime number which is 2.

No other even numbers can be prime as they will have 2 as a factor (as well as themselves and one).

What are the first 10 prime numbers?

The first ten prime numbers are...

2 3 5 7 11 13 17 19 23 29

What prime numbers are there between 1 and 100.

All the prime numbers between 1 and 100 are...

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97

There are 25 prime numbers between 1 and 100.

What is the ...th prime number?

How man prime numbers are there between....

What this shows is that as the range of numbers gets large, the density of prime numbers gets smaller.

So the prime numbers become more spread out as the numbers get larger.

Are the prime numbers infinite?

So the next question I'm betting you want to know is: "If the prime numbers become more spread out as the numbers get larger and larger, do they eventually stop?"

Well, the answer is no - prime numbers never stop they just get more and more spaced out.

The set of prime numbers is infinite and there are several different proofs to demonstrate this!

One such proof is given here on the primes.utm.edu website.

What does it mean if numbers are coprime, or co-prime?

• Two or more numbers are said to be coprime (or co-prime) if their greatest common factor (or only common factor) is 1.

If you want to see if two or more numbers are co-prime, why not try our Greatest Common Factor Calculator.

Sieve of Erastosthenes

The Sieve of Erastosthenes is a method for finding what is a prime numbers between 2 and any given number.

Eratosthenes was a Greek mathematician (as well as being a poet, an astronomer and musician) who lived from about 276BC to 194BC.

If you want to find out more about his sieve for finding primes, and print out some Sieve of Eratosthenes worksheets, use the link below.

• Sieve of Eratosthenes page

What is prime factorization?

To find out more about prime factorization, including how it works and to look at some worked examples, take a look at our prime factorization support page.

• What is Prime Factorization support page

Prime Factorization Worksheets

We have a collection of factor tree and prime factorization worksheets for students aged 6th grade and upwards.

Using factor trees is a great visual way of finding all the prime factors of a number.

We also have some problem solving, riddles and challenges on our Prime Factorization Worksheets page.

• Factor Tree Worksheets (easier)
• Prime Factorization Worksheets (harder)

Divisibility Rules Charts

If you are looking for some printable divisibility charts to help you learn you rules, then try our range here.

• Divisibility Rules 1-10 Charts

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Prime Numbers Questions

The prime numbers questions and answers are provided here for students to understand the concept quickly. Prime Numbers is one of the most basic concepts taught in primary classes. The questions framed are based on the NCERT curriculum. Students can use these questions to take a quick review of the concepts, and become familiar with the topics by practising them. Check your answers against the detailed explanations provided for each question. To learn more about prime numbers, click here .

Go through the below prime numbers questions and answers, and practise them as well.

Prime Numbers Questions with Solutions

1. The smallest prime number is _____.

The smallest prime number is 2 . The number “2” is the only even prime number, which has only two factors, such as 1 and 2.

2. What are the first 10 prime numbers?

The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

3. Is 9 a prime number?

No, the number 9 is not a prime number.

This is because the number 9 has more than 2 factors. The factors of 9 are 1, 3 and 9. Hence, we can consider 9 as a composite number.

Also, read : Composite Numbers .

4. What is the sum of the first 10 prime numbers?

As we know, the first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

Therefore, sum = 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29.

Hence, the sum of the first ten prime numbers is 129.

5. What is the mean of the first ten prime numbers?

First 10 prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

As we know, Mean = Sum of all values / Total number of values

Mean = 129 / 10

Mean = 12.9

Hence, the mean of the first ten prime numbers is 12.9.

6. What is the median of the first ten prime numbers?

As we know,

The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

The prime number sequence is already in ascending order.

So, we have 10 terms here.

Therefore, Median = Mean of 5th and 6th term

Here, 5th term = 11 and 6th term = 13.

Median = (11+13)/2 = 24/2 = 12

Hence, the median of the first ten prime numbers is 12.

7. What is the sum of the first seven prime numbers divided by 2?

We know that the first seven prime numbers are 2, 3, 5, 7, 11, 13, 17.

Therefore, sum = 2+3+5+7+11+13+17 = 58

When the sum is divided by 2, we get

Hence, the sum of the first seven prime numbers divided by 2 is 29.

8. If “p” is the prime number, find the number of factors p 2 has.

As we know, p 2 can be written as the product of p and P. (i.e., p×p). Hence, the factors of p 2 are 1, p and p 2 .

For example, let us take p = 2, the factors of 2 are 1, 2 and 4.

Therefore, p 2 has exactly three factors.

9. Identify the twin primes among the given pair of numbers:

(1, 3), (3, 5), (13, 19), (1, 2)

As know that the number 1 is neither prime nor composite. Hence, we can ignore the pairs (1, 3) and (1, 2).

As we know, twin prime numbers are the pair of prime numbers with a difference of 2.

Here, (3, 5) is a pair of prime numbers with a difference of 2 (i.e) 5 – 3 = 2.

Whereas (13, 19) is also a pair of prime numbers, in which the difference between them is not equal to 2.

Hence, (3, 5) is a twin prime.

Also, read : What are Twin Primes?

10. How many prime numbers are there between 1 and 50?

The list of prime numbers between 1 and 50 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.

Hence, the number of prime numbers between 1 and 50 is 15.

Video Lesson on Prime Numbers

Practice Questions

• What is the sum of the first 20 prime numbers?
• What is the mean of the first 50 prime numbers?
• If “p” is the prime number, find the number of factors p 3 has.
• Is 15 a prime number?
• Which is the smallest odd prime number?

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Year 5 Prime Numbers Maths Challenge

This Year 5 Prime Numbers Maths Challenge checks your child’s understanding of prime numbers while developing their problem solving ability. Children will have to apply their knowledge of prime numbers to work out where children are on a board game.

If you would like to access additional resources which link to this maths challenge, you can purchase a subscription for only £5.31 per month on our sister site, Classroom Secrets .

Teacher Specific Information

This Year 5 Prime Numbers Maths Challenge checks pupils’ understanding of prime numbers while developing their problem solving ability. Pupils will have to apply their knowledge of prime numbers to work out where children are on a board game.

National Curriculum Objectives

Calculation – multiplication and division (5C5b) Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers

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Prime numbers - Year 5 Multiplication and Division

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

5 November 2019

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This is a whole lesson based on the Year 5 Multiplication and Division objective of Prime numbers”. This resource includes the teacher input ( learning journey), independent worksheet and a depth activity to deepen the children’s understanding of the concept being learned.

The questions have been inspired and adapted from the White Rose Small Steps Guidance and Teaching for Mastery documents. This document is useful for teachers who have adapted Maths Mastery and need guidance in the approach or those who are looking for variation in fluency, reasoning and problem solving or simply those who don’t want to plan it themselves but want high quality resources and quality first teaching. =)

All of the documents that are uploaded as an Activinspire file are interactive and all of the concrete/pictorial manipulative can be used, moved and manipulated.

This document can be downloaded on Activinspire and it is also available as a PDF for those who do not have Activinspire.

Please note - these resources are not compatible with Smart Notebook and the PDF file is not interactive.

Thank you for taking the time to review my resources. =) I hope this helps you with your teaching and if it does please could you be kind enough to leave some positive feedback. =)

Kind regards,

@MasteryMaths01

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Point in Time Count in 2023 showed 110 people homeless with local expense of $5 million

Supportive services for one person can average $45,500 annually.

An entire community is impacted by housing conditions.

The whole community can be engaged in working toward housing diversity and reducing homelessness , according to speakers who addressed a wide range of housing issues at the third annual Community Meeting on Housing and Homelessness in Wayne County held at First Presbyterian Church's Bruch Hall.

One of dozens of statistics related to the topic calculated the cost of homelessness to a community based on associated hospitalization and medical treatment, mental health treatment and hospitalization , criminal justice system involvement and emergency shelter and social service supports.

A person experiencing homelessness may cost a taxpayer an average of $45,530 a year in supportive services, said James Fox, CEO of Community Action Wayne/Medina and president of the Wayne County Housing Coalition.

The Wayne County Point in Time Count − a one-day-a year county-wide tally −  held on Jan. 23, 2023, showed 110 people homeless at that time − either unsheltered, or sheltered at OneEighty, the Salvation Army or the Severe Weather Shelter − at an estimated annual local expense of about $5 million.

What "keeps me up at night," Fox said at Thursday's presentation, is the high-risk population at "imminent risk" of losing housing within 14 days because they don't have the resources or support to obtain other permanent housing.

Citizens can engage in effort to solving housing problems

Fox advocated, "Be champions of this process" of solving housing problems, referring to opportunities for citizen engagement.

Included on the list were volunteering time at the Severe Weather Shelter and donating funds, meals or supplies through Homeward Bound; becoming a landlord in Wayne Metropolitan Housing's voucher program; donating property for rehabilitation and sale through Community Action Wayne/Medina; and donating supplies and time for One Eighty's outreach programs, among others.

"We want to highlight partnerships and collaboration," Fox said. "The collaboration in this community is amazing," and not to be taken for granted.

Fox cited the misconception individuals needing housing are either not working or are lazy.

In actuality, he said, about 80% are either employed, disabled or seniors − 33% in the labor force, 23% disabled; and 27% seniors.

High number of people on housing waiting lists

Rodney Mitchell, the deputy director of Wayne Metropolitan Housing Authority, said the agency's two major programs −  public housing and Housing Choice Voucher/Section 8 − serve 900 families seeking assistance for help with rent.

Other statistics provided by Mitchell showed 13% of 791 families reporting no income; and 62% reporting receiving SSD ( Social Security disability insurance)/SSI ( supplemental security income), according to Housing Choice Voucher data.

As of March 19 of this year, 1,205 applicants were on the WCMH waiting list for Section 8 housing − 79% of whom are considered to have extremely low income; 54%, families with children; and 14%, families with disabilities.

Applicants for the public housing waiting list as of the same date totaled 1,291 − 82% with extremely low income; 38%, families with children; and 16%, families with disabilities.

In February the median home listing price in Wooster was $280,000. The average apartment rent in Wooster in April is $722 for a studio, $803 for one bedroom, $1,057 for two bedrooms and $1,062 for three bedrooms.

One of the greatest needs to address the housing problem is landlords, Mitchell said.

Other needs include supportive housing − affordable housing combined with services helping people who have chronic physical and mental health issues to maintain housing and receive appropriate health care, according to the Center on Budget and Policy Priorities.

Millea: Wooster focusing on planning 'in the area of housing'

"Housing is a separate field in and of itself," said Jonathan Millea, development coordinator for Wooster. "Economic development is another major critical need."

"(The city) care(s) very deeply about providing services," Millea said, for the housed and unhoused.

It is "focusing very much on planning, particularly in the area of housing," he said.

"Where we can, we are employing specific programs," including the Wayne County Land Bank (Wayne County Land Reutilization Corporation) to reuse delinquent and abandoned properties; the city transportation program serving between 7% and 9% of Wooster households whose members walk to and from work daily; CHIP federal grants to repair and rehabilitate homes for low-income residents; and the Community Reinvestment Area Program incentives to improve and expand properties in strategic areas and construct new housing.

"We are also focused on fair housing (for those experiencing discrimination) and property maintenance," Millea said, in addition to pursuing facilities planning for the future.

'We know we have a housing crunch'

"We know we have a housing crunch," Millea said, and are "finding new ways to welcome people into our community."

Adequate housing is needed for people employed in Wooster, he said, "and they're not finding that."

Focus areas identified for the city are the Arts, East Liberty and hospital districts; and Smithville Western and Geyers Chapel Road.

Wooster also is asking the question, "How can we encourage people to move back to the downtown area," keeping our community "occupied and vibrant," he said.

New housing is expensive, Millea said, but plays a part in lowering the tax burden overall.

"Affordable housing is the number one issue of unmet needs in our community," Fox said.

Along with the Land Bank, a "really exciting" tool is Welcome Home Ohio, he said.

Through WHO workforce housing, six to eight single family homes are planned for Rebecca Street. Future grants will fund multi-family homes and renovations in Rittman, Orville and West Salem. One of the stipulations for WHO is homes cannot sell for more than $180,000 during a 20-year compliance period.

Addition grant programs include lead abatement for 20 Wayne County properties, demolition site preparation for 11 hazardous and dilapidated properties, new construction of 10 houses for purchase by low to moderate income families and asbestos remediation for the Fredericksburg school building.

One of the new developments to be constructed is the 42-unit affordable apartment complex at 2775 Cleveland Road in Wooster.

The forum was moderated by Cindy Biggs, League of Women Voters of Wayne County; and sponsored by the League of Women Voters, Community Action Wayne/Medina, the Wooster Homelessness Task Force, Homeward Bound of Wooster and Wayne County, and the Wayne County Housing Coalition.