Year 6 Maths: Division by Factors

What is Division by Factors?

Hello Year 6! Today, we’re going to learn about division by factors. This means we will see how to divide numbers using their factors.

What are Factors?

Factors are numbers that can be multiplied together to get another number. For example, the factors of 10 are:

• 1 and 10 (because $$1 \times 10 = 10$$ )
• 2 and 5 (because $$2 \times 5 = 10$$ )

So, the factors of 10 are 1, 2, 5, and 10.

Why Do We Use Factors for Division?

When we divide a number by its factors, we can make the division easier. For instance, instead of dividing 20 by 4 directly, we can check how many times 4 is a factor of 20.

Example of Division by Factors

Let’s take the number 24. The factors of 24 are:

• 1 and 24
• 2 and 12
• 3 and 8
• 4 and 6

Now, if we want to divide 24 by 4, we can think like this:

$$24 \div 4$$

Since 4 is a factor of 24, we know that:

$$4 \times 6 = 24$$

So,

$$24 \div 4 = 6$$

Key Rules for Division by Factors

1. Identify the Factors: Always start by finding the factors of the number.
2. Check Divisibility: If the number can be divided evenly by one of its factors, then you can use that factor for division.
3. Use Simple Multiplications: Remember, division is the opposite of multiplication. If you know your multiplication tables, use them!

Tips and Tricks

• Use a Factor Tree: You can create a factor tree to help you find the factors of a number.
• Practice with Games: Use online games or flashcards to practice finding factors and dividing by them.
• Write It Down: Sometimes writing out the factors and divisions helps you see the answers more clearly.

Questions on Division by Factors

Easy Level Questions

1. What are the factors of 12?
2. Divide 18 by 3.
3. What is 20 divided by 5?
4. List the factors of 6.
5. Divide 16 by 4.
6. What are the factors of 15?
7. Divide 25 by 5.
8. What is 30 divided by 6?
9. List the factors of 8.
10. Divide 24 by 8.

Medium Level Questions

11. What are the factors of 36?
12. Divide 45 by 9.
13. What is 56 divided by 7?
14. List the factors of 28.
15. Divide 49 by 7.
16. What are the factors of 40?
17. Divide 63 by 9.
18. What is 72 divided by 8?
19. List the factors of 50.
20. Divide 81 by 9.

Hard Level Questions

21. What are the factors of 100?
22. Divide 144 by 12.
23. What is 120 divided by 10?
24. List the factors of 60.
25. Divide 98 by 14.
26. What are the factors of 81?
27. Divide 225 by 15.
28. What is 150 divided by 25?
29. List the factors of 90.
30. Divide 256 by 16.

Answers and Explanations

Easy Level Answers

1. Factors of 12: 1, 2, 3, 4, 6, 12
2. $$18 \div 3 = 6$$
3. $$20 \div 5 = 4$$
4. Factors of 6: 1, 2, 3, 6
5. $$16 \div 4 = 4$$
6. Factors of 15: 1, 3, 5, 15
7. $$25 \div 5 = 5$$
8. $$30 \div 6 = 5$$
9. Factors of 8: 1, 2, 4, 8
10. $$24 \div 8 = 3$$

Medium Level Answers

11. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
12. $$45 \div 9 = 5$$
13. $$56 \div 7 = 8$$
14. Factors of 28: 1, 2, 4, 7, 14, 28
15. $$49 \div 7 = 7$$
16. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
17. $$63 \div 9 = 7$$
18. $$72 \div 8 = 9$$
19. Factors of 50: 1, 2, 5, 10, 25, 50
20. $$81 \div 9 = 9$$

Hard Level Answers

21. Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
22. $$144 \div 12 = 12$$
23. $$120 \div 10 = 12$$
24. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
25. $$98 \div 14 = 7$$
26. Factors of 81: 1, 3, 9, 27, 81
27. $$225 \div 15 = 15$$
28. $$150 \div 25 = 6$$
29. Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
30. $$256 \div 16 = 16$$

I hope this helps you understand division by factors better! Keep practicing, and you’ll be a division expert in no time!