Introduction to Factors

Hello, Year 5! Today, we are going to learn about factors and how we can use them in an informal way to help us with our maths problems. Let’s dive right in!

What are Factors?

Factors are numbers that you can multiply together to get another number. For example, if we have the number 12, the factors of 12 are:

  • 1 and 12 (because 1 × 12 = 12)
  • 2 and 6 (because 2 × 6 = 12)
  • 3 and 4 (because 3 × 4 = 12)

So, the factors of 12 are 1, 2, 3, 4, 6, and 12.

Why Use Factors?

Using factors can help us simplify multiplication and division. It makes it easier to find answers without doing long calculations.

For example, if you want to multiply 16 by 3, you can break 16 down into its factors. The factors of 16 are 1, 2, 4, 8, and 16. You could choose to use 4 and 4:

$$

16 = 4 \times 4

$$

Then multiply:

$$

4 \times 3 = 12

$$

$$

4 \times 3 = 12

$$

Finally, add the two results together:

$$

12 + 12 = 24

$$

So, 16 × 3 = 48!

Key Rules for Using Factors

  1. Know Your Times Tables: It’s important to know your multiplication facts well. This will help you find factors quickly.
  2. Break Down Numbers: Look for simpler numbers that multiply together to make the number you are working with.
  3. Use Addition: When you break numbers into factors, sometimes you will need to add results together.
  4. Check Your Work: After you find your answer, you can multiply back to see if it matches the original problem.

Tips and Tricks

  • Practice with Small Numbers: Start with smaller numbers to get used to finding factors.
  • Use a Factor Tree: You can draw a factor tree to help break down numbers into their prime factors. This is a fun and visual way to see how numbers work!
  • Group Numbers: When multiplying, try to group factors that are easy to work with.

Practice Questions

Easy Level Questions

  1. What are the factors of 10?
  2. What are the factors of 15?
  3. What are the factors of 6?
  4. What are the factors of 8?
  5. What are the factors of 5?
  6. What are the factors of 9?
  7. What are the factors of 12?
  8. What are the factors of 14?
  9. What are the factors of 16?
  10. What are the factors of 18?

Medium Level Questions

  1. Find the factors of 20.
  2. Find the factors of 21.
  3. Find the factors of 24.
  4. What two factors of 30 add up to 11?
  5. What two factors of 28 can be multiplied to give 28?
  6. Find the factors of 25.
  7. Find the factors of 36.
  8. What two factors of 40 can be added to give 12?
  9. What two factors of 42 can be multiplied to give 84?
  10. Find the factors of 48.

Hard Level Questions

  1. Find all the factors of 60.
  2. Which two factors of 72 multiply to give 144?
  3. Find the common factors of 30 and 45.
  4. Find the prime factors of 36.
  5. What two factors of 50 add up to 25?
  6. Find all the factors of 84.
  7. What are the factors of 100?
  8. Find the prime factors of 60.
  9. Find all the factors of 120.
  10. Which two factors of 56 multiply to give 112?

Answers and Explanations

Easy Level Answers

  1. 1, 2, 5, 10
  2. 1, 3, 5, 15
  3. 1, 2, 3, 6
  4. 1, 2, 4, 8
  5. 1, 5
  6. 1, 3, 9
  7. 1, 2, 3, 4, 6, 12
  8. 1, 2, 7, 14
  9. 1, 2, 4, 8, 16
  10. 1, 2, 3, 6, 9, 18

Medium Level Answers

  1. 1, 2, 4, 5, 10, 20
  2. 1, 3, 7, 21
  3. 1, 2, 3, 4, 6, 8, 12, 24
  4. 2 and 5
  5. 4 and 7
  6. 1, 5, 25
  7. 1, 2, 3, 4, 6, 9, 12, 18, 36
  8. 4 and 8
  9. 6 and 14
  10. 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Hard Level Answers

  1. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  2. 8 and 9
  3. 1, 3, 5
  4. 2 × 2 × 3
  5. 10 and 5
  6. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
  7. 1, 2, 4, 5, 10, 20, 25, 50, 100
  8. 2 × 2 × 3 × 5
  9. 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, 60, 120
  10. 7 and 8

Great job, Year 5! Keep practicing those factors, and you’ll become a maths whizz in no time!