Introduction to Factors and Multiples

Hello Year 5! Today, we are going to explore the exciting world of factors and multiples. These are important concepts in maths that will help you with many other topics, so let’s dive in!

What are Factors?

Factors are numbers that can be multiplied together to get another number. In simpler terms, if you can divide a number by another number without leaving a remainder, then the second number is a factor of the first.

Example:

Let’s look at the number 12. The factors of 12 are the numbers that can divide 12 evenly.

  • 1 × 12 = 12
  • 2 × 6 = 12
  • 3 × 4 = 12

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

What are Multiples?

Multiples are what you get when you multiply a number by another whole number. In other words, if you take a number and keep adding it to itself, you get its multiples.

Example:

Let’s look at the number 3. The first few multiples of 3 are:

  • 3 × 1 = 3
  • 3 × 2 = 6
  • 3 × 3 = 9
  • 3 × 4 = 12
  • 3 × 5 = 15

So, the first five multiples of 3 are: 3, 6, 9, 12, and 15.

Key Rules for Factors and Multiples

  1. Factors of a number are always less than or equal to that number.
  2. 1 is a factor of every number.
  3. The number itself is always a factor.
  4. Multiples of a number can be found by multiplying that number by 1, 2, 3, and so on.
  5. 0 is a multiple of every number.

Tips and Tricks

  • To find factors, start with 1 and the number itself, then test each number in between to see if it divides evenly.
  • To find multiples, just keep adding the number (or multiplying by whole numbers).
  • It’s helpful to remember that every number has at least two factors: 1 and the number itself.

Questions on Factors and Multiples

Let’s practice what we’ve learned!

Easy Level Questions

  1. What are the factors of 10?
  2. What are the multiples of 2 up to 20?
  3. Is 5 a factor of 25?
  4. What is the smallest multiple of 7?
  5. What are the factors of 15?
  6. What are the first three multiples of 4?
  7. Is 6 a factor of 36?
  8. What are the multiples of 5 up to 30?
  9. How many factors does the number 8 have?
  10. What is the largest multiple of 3 less than 20?
  11. What are the factors of 18?
  12. What are the first five multiples of 6?
  13. Is 9 a factor of 81?
  14. What is the smallest multiple of 10?
  15. What are the factors of 20?
  16. What are the multiples of 9 up to 45?
  17. Is 12 a factor of 144?
  18. What is the largest multiple of 2 less than 50?
  19. What are the factors of 30?
  20. What are the first four multiples of 8?

Medium Level Questions

  1. List all the factors of 24.
  2. Find the first five multiples of 7.
  3. Is 3 a factor of 27?
  4. What are the common multiples of 2 and 3 up to 30?
  5. How many factors does the number 36 have?
  6. What is the smallest multiple of 11 greater than 50?
  7. Find all the factors of 40.
  8. What are the first six multiples of 5?
  9. Is 15 a factor of 225?
  10. What is the largest multiple of 4 less than 100?
  11. How many multiples of 6 are there between 1 and 60?
  12. Find the factors of 50.
  13. What are the first four multiples of 12?
  14. Is 8 a factor of 64?
  15. What is the smallest multiple of 9 greater than 30?
  16. List the factors of 32.
  17. What are the common multiples of 4 and 5 up to 40?
  18. How many factors does the number 50 have?
  19. What is the largest multiple of 3 less than 100?
  20. Find the factors of 45.

Hard Level Questions

  1. List all the factors of 60.
  2. Find the first ten multiples of 8.
  3. How many factors does the number 72 have?
  4. What are the common multiples of 6 and 8 up to 48?
  5. Is 18 a factor of 306?
  6. What is the smallest multiple of 13 greater than 100?
  7. Find the factors of 84.
  8. What are the first five multiples of 15?
  9. Is 20 a factor of 400?
  10. What is the largest multiple of 7 less than 200?
  11. How many multiples of 9 are there between 1 and 90?
  12. Find the factors of 100.
  13. What are the first six multiples of 11?
  14. Is 14 a factor of 196?
  15. What is the smallest multiple of 12 greater than 80?
  16. List the factors of 96.
  17. What are the common multiples of 3 and 5 up to 60?
  18. How many factors does the number 120 have?
  19. What is the largest multiple of 5 less than 200?
  20. Find the factors of 225.

Answers

Easy Level Answers

  1. 1, 2, 5, 10
  2. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
  3. Yes
  4. 7
  5. 1, 3, 5, 15
  6. 4, 8, 12
  7. Yes
  8. 5, 10, 15, 20, 25, 30
  9. 1, 2, 4, 8
  10. 18
  11. 1, 2, 3, 6, 9, 18
  12. 6, 12, 18, 24, 30
  13. Yes
  14. 10
  15. 1, 2, 4, 5, 10, 20
  16. 9, 18, 27, 36, 45
  17. Yes
  18. 1, 2, 4, 5, 10, 20, 25, 50
  19. 15
  20. 8, 16, 24

Medium Level Answers

  1. 1, 2, 3, 4, 6, 8, 12, 24
  2. 7, 14, 21, 28, 35
  3. Yes
  4. 6, 12, 18, 24, 30
  5. 6
  6. 55
  7. 1, 2, 4, 5, 8, 10, 20, 40
  8. 5, 10, 15, 20, 25, 30
  9. Yes
  10. 96
  11. 10
  12. 1, 2, 5, 10, 20, 25, 50
  13. 12, 24, 36, 48
  14. Yes
  15. 84
  16. 1, 2, 4, 8, 16, 32
  17. 20, 40
  18. 6
  19. 99
  20. 1, 3, 5, 9, 15, 25

Hard Level Answers

  1. 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  2. 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
  3. 12
  4. 24
  5. Yes
  6. 104
  7. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
  8. 15, 30, 45, 60, 75
  9. Yes
  10. 196
  11. 10
  12. 1, 2, 4, 5, 10, 20, 25, 50
  13. 11, 22, 33, 44, 55, 66
  14. Yes
  15. 84
  16. 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
  17. 15, 30, 45
  18. 16
  19. 195
  20. 1, 3, 5, 9, 15, 25

I hope you enjoyed learning about factors and multiples! Keep practicing, and you’ll become a pro in no time!