Year 5 Maths: Using Factors to Multiply

Understanding Factors

Hello, Year 5! Today, we’re going to learn about factors and how we can use them to help us multiply numbers more easily.

What are Factors?

A factor is a number that can be divided evenly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12 because:

• $$12 \div 1 = 12$$
• $$12 \div 2 = 6$$
• $$12 \div 3 = 4$$
• $$12 \div 4 = 3$$
• $$12 \div 6 = 2$$
• $$12 \div 12 = 1$$

Why Use Factors to Multiply?

Using factors can help us break down larger multiplication problems into smaller, easier ones. This makes it simpler to find the answer!

How to Use Factors to Multiply

1. Find the factors of one of the numbers.
2. Multiply one factor by the other number.
3. Repeat until all factors have been used.
4. Add up the results if necessary.

Example

Let’s look at the multiplication problem

1. We can break down the number 6 into its factors: $$2 \times 3$$ .
2. Now, we can use these factors to multiply:
   • First, multiply $$2 \times 4 = 8$$
   • Then, multiply $$3 \times 4 = 12$$
3. Now we can add the two results together: $$8 + 12 = 20$$ .
4. So, $$6 \times 4 = 24$$ .

Key Rules

• Always look for easy factors that can make multiplication simpler.
• Remember to multiply each factor by the other number.
• Don’t forget to check your work!

Tips and Tricks

• Skip Counting: You can also use skip counting to help with larger numbers.
• Visual Aids: Using arrays can help you visualize how factors work.
• Practice: The more you practice, the easier it becomes!

Questions

Easy Level Questions

1. What are the factors of 10?
2. Multiply: $$2 \times 3$$
3. What are the factors of 8?
4. Multiply: $$5 \times 1$$
5. What are the factors of 6?
6. Multiply: $$4 \times 2$$
7. What are the factors of 12?
8. Multiply: $$3 \times 3$$
9. What are the factors of 15?
10. Multiply: $$1 \times 7$$
11. What are the factors of 9?
12. Multiply: $$2 \times 5$$
13. What are the factors of 14?
14. Multiply: $$6 \times 1$$
15. What are the factors of 16?
16. Multiply: $$3 \times 2$$
17. What are the factors of 4?
18. Multiply: $$2 \times 6$$
19. What are the factors of 18?
20. Multiply: $$7 \times 0$$

Medium Level Questions

1. What are the factors of 20?
2. Multiply: $$5 \times 6$$
3. Find the product of the factors of 12.
4. Multiply: $$3 \times 7$$
5. What are the factors of 24?
6. Multiply: $$4 \times 5$$
7. Find the product of the factors of 16.
8. Multiply: $$2 \times 9$$
9. What are the factors of 30?
10. Multiply: $$6 \times 2$$
11. Find the product of the factors of 18.
12. Multiply: $$5 \times 4$$
13. What are the factors of 36?
14. Multiply: $$3 \times 5$$
15. Find the product of the factors of 28.
16. Multiply: $$8 \times 2$$
17. What are the factors of 32?
18. Multiply: $$7 \times 3$$
19. Find the product of the factors of 25.
20. Multiply: $$9 \times 2$$

Hard Level Questions

1. What are the factors of 42?
2. Calculate: $$6 \times 7$$ using factors.
3. What are the factors of 48?
4. Calculate: $$8 \times 5$$ using factors.
5. What are the factors of 54?
6. Calculate: $$9 \times 6$$ using factors.
7. What are the factors of 60?
8. Calculate: $$12 \times 5$$ using factors.
9. What are the factors of 70?
10. Calculate: $$10 \times 4$$ using factors.
11. What are the factors of 81?
12. Calculate: $$15 \times 3$$ using factors.
13. What are the factors of 72?
14. Calculate: $$18 \times 4$$ using factors.
15. What are the factors of 90?
16. Calculate: $$7 \times 12$$ using factors.
17. What are the factors of 100?
18. Calculate: $$11 \times 9$$ using factors.
19. What are the factors of 36?
20. Calculate: $$14 \times 5$$ using factors.

Answers

Easy Level Answers

1. 1, 2, 5, 10
2. 6
3. 1, 2, 4, 8
4. 5
5. 1, 2, 3, 6
6. 8
7. 1, 2, 3, 4, 6, 12
8. 9
9. 1, 3, 5, 15
10. 7
11. 1, 3, 9
12. 10
13. 1, 2, 7, 14
14. 6
15. 1, 2, 4, 8, 16
16. 6
17. 1, 2, 3, 6, 9, 18
18. 12
19. 1, 2, 3, 6, 9, 18
20. 0

Medium Level Answers

1. 1, 2, 4, 5, 10, 20
2. 30
3. 1, 2, 3, 4, 6, 12
4. 21
5. 1, 2, 3, 4, 6, 8, 12, 24
6. 20
7. 1, 2, 4, 8, 16
8. 18
9. 1, 2, 3, 5, 6, 10, 15, 30
10. 12
11. 1, 2, 3, 6, 9, 18
12. 20
13. 1, 2, 3, 4, 6, 9, 12, 18, 36
14. 15
15. 1, 2, 4, 7, 14, 28
16. 16
17. 1, 2, 4, 8, 16
18. 21
19. 1, 5, 25
20. 18

Hard Level Answers

1. 1, 2, 3, 6, 7, 14, 21, 42
2. 42
3. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
4. 40
5. 1, 2, 3, 6, 9, 18, 27, 54
6. 54
7. 1, 2, 3, 4, 5, 6, 7, 10, 12, 15, 20, 30, 60
8. 60
9. 1, 2, 5, 7, 10, 14, 18, 21, 30, 35, 42, 70
10. 40
11. 1, 3, 9, 27, 81
12. 45
13. 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
14. 72
15. 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
16. 84
17. 1, 2, 4, 5, 10, 20, 25, 50, 100
18. 99
19. 1, 2, 3, 4, 6, 9, 12, 18, 24, 36
20. 70

I hope this helps you understand how to use factors to multiply better! Keep practicing, and you’ll see how easy it can be!