Year 5 Maths: Factor Trees

What is a Factor Tree?

A factor tree is a simple way to break down a number into its factors. Factors are the numbers that you can multiply together to get the original number. A factor tree helps us see how a number can be divided into smaller parts.

How to Create a Factor Tree

1. Start with a Number: Begin with any number you want to factor.
2. Find Two Factors: Find two numbers that multiply together to make that number.
3. Repeat: Take one of those factors and break it down again into two factors. Keep doing this until you reach the number 1 or a prime number (a number that can only be divided by 1 and itself).
4. Draw the Tree: You can draw branches like a tree to show how the number splits into factors.

Example: Factor Tree for 12

1. Start with 12.
2. Find two factors: 3 and 4 (because $$3 \times 4 = 12$$ ).
3. Now, break down 4 into 2 and 2 (because $$2 \times 2 = 4$$ ).
4. 3 is a prime number, so we stop there.

Here’s how it looks:

       12      /  \     3    4          / \         2   2 

So, the prime factorization of 12 is

Key Rules for Factor Trees

1. Every number can be broken down: All numbers can be expressed as a product of prime numbers.
2. Stopping point: You stop breaking down when you reach 1 or a prime number.
3. Order doesn’t matter: The order of factors does not change the product.

Tips and Tricks

• Know your times tables: This will help you find factors quicker.
• Use the smallest factors first: Begin with the smallest numbers (like 2, 3, 5) to make it easier.
• Practice with different numbers: The more you practice, the better you’ll get!

Questions

Easy Level (20 questions)

1. Create a factor tree for 6.
2. What are the factors of 8?
3. Find two factors of 9.
4. Create a factor tree for 15.
5. What are the prime factors of 10?
6. Draw a factor tree for 20.
7. What are the factors of 12?
8. Create a factor tree for 18.
9. What are the prime factors of 14?
10. Draw a factor tree for 16.
11. What two factors multiply to make 3?
12. Find two factors of 4.
13. Create a factor tree for 5.
14. What are the factors of 2?
15. Draw a factor tree for 24.
16. What are the prime factors of 21?
17. Create a factor tree for 30.
18. What are the factors of 1?
19. Find two factors of 25.
20. Draw a factor tree for 36.

Medium Level (20 questions)

1. Create a factor tree for 24.
2. What are the prime factors of 28?
3. Draw a factor tree for 45.
4. What two factors multiply to make 12?
5. Find the prime factorization of 50.
6. Create a factor tree for 60.
7. What are the factors of 42?
8. Draw a factor tree for 56.
9. What are the prime factors of 32?
10. Create a factor tree for 72.
11. What two numbers multiply to make 84?
12. Find two factors of 36.
13. Create a factor tree for 90.
14. What are the factors of 18?
15. Draw a factor tree for 100.
16. What are the prime factors of 81?
17. Create a factor tree for 48.
18. What two factors multiply to make 70?
19. Find the prime factorization of 64.
20. Draw a factor tree for 96.

Hard Level (20 questions)

1. Create a factor tree for 84.
2. What are the prime factors of 120?
3. Draw a factor tree for 144.
4. What two factors multiply to make 96?
5. Find the prime factorization of 150.
6. Create a factor tree for 200.
7. What are the factors of 72?
8. Draw a factor tree for 225.
9. What are the prime factors of 63?
10. Create a factor tree for 300.
11. What two numbers multiply to make 175?
12. Find two factors of 225.
13. Create a factor tree for 360.
14. What are the factors of 81?
15. Draw a factor tree for 450.
16. What are the prime factors of 500?
17. Create a factor tree for 600.
18. What two factors multiply to make 840?
19. Find the prime factorization of 720.
20. Draw a factor tree for 960.

Answers

Easy Level Answers

1. 6: $$2 \times 3$$
2. Factors of 8: 1, 2, 4, 8
3. Factors of 9: 1, 3, 9
4. 15: $$3 \times 5$$
5. Prime factors of 10: $$2 \times 5$$
6. 20: $$2 \times 2 \times 5$$
7. Factors of 12: 1, 2, 3, 4, 6, 12
8. 18: $$2 \times 3 \times 3$$
9. Prime factors of 14: $$2 \times 7$$
10. 16: $$2 \times 2 \times 2 \times 2$$
11. Factors of 3: 1, 3
12. Factors of 4: 1, 2, 4
13. 5: $$5$$
14. Factors of 2: 1, 2
15. 24: $$2 \times 2 \times 2 \times 3$$
16. Prime factors of 21: $$3 \times 7$$
17. 30: $$2 \times 3 \times 5$$
18. Factors of 1: 1
19. Factors of 25: 1, 5, 25
20. 36: $$2 \times 2 \times 3 \times 3$$

Medium Level Answers

1. 24: $$2 \times 2 \times 2 \times 3$$
2. Prime factors of 28: $$2 \times 2 \times 7$$
3. 45: $$3 \times 3 \times 5$$
4. Factors of 12: 1, 2, 3, 4, 6, 12
5. Prime factorization of 50: $$2 \times 5 \times 5$$
6. 60: $$2 \times 2 \times 3 \times 5$$
7. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
8. 56: $$2 \times 2 \times 2 \times 7$$
9. Prime factors of 32: $$2 \times 2 \times 2 \times 2 \times 2$$
10. 72: $$2 \times 2 \times 2 \times 3 \times 3$$
11. Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
12. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
13. 90: $$2 \times 3 \times 3 \times 5$$
14. Factors of 18: 1, 2, 3, 6, 9, 18
15. 100: $$2 \times 2 \times 5 \times 5$$
16. Prime factors of 81: $$3 \times 3 \times 3 \times 3$$
17. 48: $$2 \times 2 \times 2 \times 2 \times 3$$
18. Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70
19. Prime factorization of 64: $$2 \times 2 \times 2 \times 2 \times 2 \times 2$$
20. 96: $$2 \times 2 \times 2 \times 2 \times 2 \times 3$$

Hard Level Answers

1. 84: $$2 \times 2 \times 3 \times 7$$
2. Prime factors of 120: $$2 \times 2 \times 2 \times 3 \times 5$$
3. 144: $$2 \times 2 \times 2 \times 2 \times 3 \times 3$$
4. Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
5. Prime factorization of 150: $$2 \times 3 \times 5 \times 5$$
6. 200: $$2 \times 2 \times 2 \times 5 \times 5$$
7. Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
8. 225: $$3 \times 3 \times 5 \times 5$$
9. Prime factors of 63: $$3 \times 3 \times 7$$
10. 300: $$2 \times 2 \times 3 \times 5 \times 5$$
11. Factors of 175: 1, 5, 7, 25, 35, 175
12. Factors of 225: 1, 3, 5, 9, 15, 25, 45, 75, 225
13. 360: $$2 \times 2 \times 2 \times 3 \times 3 \times 5$$
14. Factors of 81: 1, 3, 9, 27, 81
15. 450: $$2 \times 3 \times 3 \times 5 \times 5$$
16. Prime factors of 500: $$2 \times 2 \times 5 \times 5 \times 5$$
17. 600: $$2 \times 2 \times 2 \times 3 \times 5 \times 5$$
18. Factors of 840: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
19. Prime factorization of 720: $$2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 5$$
20. 960: $$2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 5$$

Feel free to ask questions if you need more help understanding factor trees! Happy factoring!