Year 5 Maths: Prime Factors

What are Prime Factors?

Hello, Year 5! Today, we’re going to learn about prime factors. But what exactly are they?

Prime numbers are special numbers that can only be divided by 1 and themselves. For example, the number 5 is a prime number because the only numbers that can go into it evenly are 1 and 5.

Factors are numbers that can be multiplied together to get another number. So, when we talk about prime factors, we mean the prime numbers that multiply together to make a certain number.

Examples

Let’s look at an example:

Example 1: The number 12

1. First, we need to find all the factors of 12. They are: 1, 2, 3, 4, 6, and 12.
2. Now, we identify which of these factors are prime. The prime factors of 12 are 2 and 3 because:
   • 2 is a prime number (only divisible by 1 and 2).
   • 3 is also a prime number (only divisible by 1 and 3).
3. So, the prime factorization of 12 is: $$2 \times 2 \times 3$$ or in prime factors: $$2^2 \times 3$$ .

Example 2: The number 30

1. The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
2. The prime factors are 2, 3, and 5.
3. Therefore, the prime factorization of 30 is: $$2 \times 3 \times 5$$ .

Key Rules

1. Prime Numbers: Remember, a prime number is only divisible by 1 and itself.
2. Finding Prime Factors: Start by listing all factors, then identify which of them are prime.
3. Product of Prime Factors: When you multiply all the prime factors together, you should get back to the original number.

Tips and Tricks

• Divide and Conquer: Start dividing the number by the smallest prime (2) and keep going until you can’t divide anymore.
• Factor Tree: Draw a tree to break down the number into its prime factors. Start with the number at the top and split it into two factors, then repeat this for each factor until you only have prime numbers.

Here’s how a factor tree for 30 looks:

       30      /  \     3    10         /  \        2    5 

From this tree, we can see the prime factors are 2, 3, and 5.

Questions

Easy Level Questions

1. What are the prime factors of 10?
2. List the prime factors of 15.
3. What is a prime number?
4. Is 7 a prime number? Yes or No?
5. What are the prime factors of 8?
6. List all factors of 6.
7. What are the prime factors of 18?
8. Is 4 a prime number? Yes or No?
9. What are the prime factors of 21?
10. Can you name a prime number between 1 and 10?
11. What are the prime factors of 24?
12. Is 9 a prime number? Yes or No?
13. What are the prime factors of 25?
14. List the factors of 9.
15. What is the smallest prime number?
16. List the prime factors of 14.
17. Can a prime number be even? Yes or No?
18. What are the prime factors of 16?
19. What is the prime factorization of 22?
20. Is 1 a prime number? Yes or No?

Medium Level Questions

1. What is the prime factorization of 36?
2. Find the prime factors of 45.
3. What are the prime factors of 50?
4. List the prime factors of 60.
5. What is the prime factorization of 28?
6. What are the prime factors of 32?
7. Find the prime factorization of 72.
8. What are all the factors of 100?
9. What are the prime factors of 42?
10. Can you find the prime factors of 90?
11. What is the prime factorization of 48?
12. Find the prime factors of 70.
13. What is the prime factorization of 54?
14. List the factors of 81.
15. What are the prime factors of 36?
16. What is the prime factorization of 64?
17. Find the prime factors of 99.
18. What are all the factors of 88?
19. What is the prime factorization of 56?
20. Find the prime factors of 72.

Hard Level Questions

1. What is the prime factorization of 144?
2. Find the prime factors of 120.
3. What is the prime factorization of 150?
4. List the prime factors of 180.
5. What are the prime factors of 200?
6. Find the prime factorization of 225.
7. What are the prime factors of 210?
8. Calculate the prime factorization of 256.
9. What is the prime factorization of 300?
10. Find the prime factors of 360.
11. What are all the factors of 400?
12. What is the prime factorization of 480?
13. List the prime factors of 500.
14. Find the prime factorization of 625.
15. What is the prime factorization of 729?
16. What are all the factors of 800?
17. Calculate the prime factorization of 900.
18. What are the prime factors of 1024?
19. What is the prime factorization of 1100?
20. Find the prime factors of 1152.

Answers

Easy Level Answers

1. 2, 5
2. 3, 5
3. A number that can only be divided by 1 and itself.
4. Yes
5. 2
6. 1, 2, 3, 6
7. 2, 3
8. No
9. 3, 7
10. 2, 3, 5, 7
11. 2, 3
12. No
13. 5
14. 1, 3, 9
15. 2
16. 2, 7
17. Yes, only the number 2 is even.
18. 2
19. 2, 11
20. No

Medium Level Answers

1. 2^2 × 3^2
2. 3^2 × 5
3. 2 × 5^2
4. 2^2 × 3 × 5
5. 2^2 × 7
6. 2^5
7. 2^3 × 3^2
8. 1, 2, 4, 5, 10, 20, 25, 50, 100
9. 2, 3, 7
10. 2, 3, 5
11. 2^3 × 3
12. 2 × 5 × 7
13. 2 × 3^3
14. 1, 3, 9, 27
15. 2^2 × 7
16. 2 × 5
17. 3^2 × 5
18. 2^4 × 5
19. 2^2 × 5^2
20. 2^3 × 3^2

Hard Level Answers

1. 2^4 × 3^2
2. 2^3 × 3 × 5
3. 2 × 3 × 5^2
4. 2^2 × 3^2 × 5
5. 2^3 × 5^2
6. 3^2 × 5^2
7. 2 × 3 × 5 × 7
8. 2^8
9. 2^2 × 3 × 5^2
10. 2^3 × 3^2 × 5
11. 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200, 400
12. 2^4 × 3 × 5
13. 2^2 × 5^3
14. 5^4
15. 3^6
16. 2^5 × 5^2
17. 2^2 × 3^2
18. 2^10
19. 2^2 × 5^2 × 11
20. 2^4 × 3^2

I hope you enjoyed learning about prime factors! Keep practicing, and soon you’ll be a prime factor expert!