What are Factor Pairs?

Hello Year 5! Today, we’re going to talk about something really cool in maths called factor pairs.

What is a Factor?

First, let’s understand what a factor is. A factor is a number that can be multiplied by another number to get a larger number. For example, if we take the number 6, we can find its factors by asking: “What numbers can I multiply together to make 6?”

The factors of 6 are:

  • 1 x 6
  • 2 x 3

So, the numbers 1, 2, 3, and 6 are all factors of 6.

What are Factor Pairs?

Now, a factor pair is simply two factors that, when multiplied together, give you a certain number. Using our example of 6, we can see that the factor pairs are:

  • (1, 6)
  • (2, 3)

Key Rules for Finding Factor Pairs

  1. Multiply to Check: If you think you’ve found a factor pair, multiply the two numbers together. If they equal the original number, you’ve done it right!
  2. Start Small: Begin by checking the smallest numbers first. Start with 1 and go up to the number itself.
  3. List All Pairs: Don’t forget to list all the pairs. Some numbers have more factor pairs than others!

Tips and Tricks

  • Even Numbers: Remember, even numbers will always have 1, 2, and themselves as factors.
  • Odd Numbers: Odd numbers will not have 2 as a factor since they cannot be divided evenly by 2.
  • Square Numbers: Numbers like 1, 4, 9, and 16 are special because they have a factor that repeats (for example, 4 can be made by 2 x 2).

Visualising Factor Pairs

You can think of factor pairs like pairs of shoes. Just like each shoe needs its partner, each factor needs its pair to make the full number!

Questions on Factor Pairs

Easy Level (20 Questions)

  1. What are the factor pairs of 8?
  2. List the factor pairs of 10.
  3. Find the factor pairs of 12.
  4. What are the factor pairs of 15?
  5. List the factor pairs of 18.
  6. Find the factor pairs of 20.
  7. What are the factor pairs of 21?
  8. List the factor pairs of 24.
  9. Find the factor pairs of 25.
  10. What are the factor pairs of 30?
  11. List the factor pairs of 32.
  12. Find the factor pairs of 36.
  13. What are the factor pairs of 40?
  14. List the factor pairs of 42.
  15. Find the factor pairs of 45.
  16. What are the factor pairs of 48?
  17. List the factor pairs of 50.
  18. Find the factor pairs of 54.
  19. What are the factor pairs of 56?
  20. List the factor pairs of 60.

Medium Level (20 Questions)

  1. What are the factor pairs of 16?
  2. Find the factor pairs of 28.
  3. List the factor pairs of 33.
  4. What are the factor pairs of 63?
  5. Find the factor pairs of 72.
  6. What are the factor pairs of 80?
  7. List the factor pairs of 90.
  8. What are the factor pairs of 100?
  9. Find the factor pairs of 110.
  10. What are the factor pairs of 120?
  11. List the factor pairs of 125.
  12. What are the factor pairs of 144?
  13. Find the factor pairs of 150.
  14. What are the factor pairs of 160?
  15. List the factor pairs of 168.
  16. What are the factor pairs of 180?
  17. Find the factor pairs of 196.
  18. What are the factor pairs of 200?
  19. List the factor pairs of 225.
  20. What are the factor pairs of 240?

Hard Level (20 Questions)

  1. What are the factor pairs of 256?
  2. Find the factor pairs of 300.
  3. List the factor pairs of 324.
  4. What are the factor pairs of 400?
  5. Find the factor pairs of 441.
  6. What are the factor pairs of 484?
  7. List the factor pairs of 576.
  8. What are the factor pairs of 625?
  9. Find the factor pairs of 729.
  10. What are the factor pairs of 800?
  11. List the factor pairs of 900.
  12. What are the factor pairs of 1024?
  13. Find the factor pairs of 1210.
  14. What are the factor pairs of 1296?
  15. List the factor pairs of 1440.
  16. What are the factor pairs of 1680?
  17. Find the factor pairs of 1800.
  18. What are the factor pairs of 2000?
  19. List the factor pairs of 2200.
  20. What are the factor pairs of 2400?

Answers to Questions

Easy Level Answers

  1. (1, 8), (2, 4)
  2. (1, 10), (2, 5)
  3. (1, 12), (2, 6), (3, 4)
  4. (1, 15), (3, 5)
  5. (1, 18), (2, 9), (3, 6)
  6. (1, 20), (2, 10), (4, 5)
  7. (1, 21), (3, 7)
  8. (1, 24), (2, 12), (3, 8), (4, 6)
  9. (1, 25), (5, 5)
  10. (1, 30), (2, 15), (3, 10), (5, 6)
  11. (1, 32), (2, 16), (4, 8)
  12. (1, 36), (2, 18), (3, 12), (4, 9), (6, 6)
  13. (1, 40), (2, 20), (4, 10), (5, 8)
  14. (1, 42), (2, 21), (3, 14), (6, 7)
  15. (1, 45), (3, 15), (5, 9)
  16. (1, 48), (2, 24), (3, 16), (4, 12), (6, 8)
  17. (1, 50), (2, 25), (5, 10)
  18. (1, 54), (2, 27), (3, 18), (6, 9)
  19. (1, 56), (2, 28), (4, 14), (7, 8)
  20. (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), (6, 10)

Medium Level Answers

  1. (1, 16), (2, 8), (4, 4)
  2. (1, 28), (2, 14), (4, 7)
  3. (1, 33), (3, 11)
  4. (1, 63), (3, 21), (7, 9)
  5. (1, 72), (2, 36), (3, 24), (4, 18), (6, 12), (8, 9)
  6. (1, 80), (2, 40), (4, 20), (5, 16), (8, 10)
  7. (1, 90), (2, 45), (3, 30), (5, 18), (9, 10)
  8. (1, 100), (2, 50), (4, 25), (5, 20), (10, 10)
  9. (1, 110), (2, 55)
  10. (1, 120), (2, 60), (3, 40), (4, 30), (5, 24), (6, 20), (8, 15), (10, 12)
  11. (1, 125), (5, 25)
  12. (1, 144), (2, 72), (3, 48), (4, 36), (6, 24), (8, 18), (9, 16), (12, 12)
  13. (1, 150), (2, 75), (3, 50), (5, 30), (6, 25), (10, 15)
  14. (1, 160), (2, 80), (4, 40), (5, 32), (8, 20), (10, 16)
  15. (1, 168), (2, 84), (3, 56), (4, 42), (6, 28), (7, 24), (8, 21), (12, 14)
  16. (1, 180), (2, 90), (3, 60), (4, 45), (5, 36), (6, 30), (9, 20), (10, 18)
  17. (1, 196), (2, 98), (4, 49)
  18. (1, 200), (2, 100), (4, 50), (5, 40), (8, 25), (10, 20)
  19. (1, 225), (3, 75), (5, 45), (9, 25), (15, 15)
  20. (1, 240), (2, 120), (3, 80), (4, 60), (5, 48), (6, 40), (8, 30), (10, 24), (12, 20), (15, 16)

Hard Level Answers

  1. (1, 256), (2, 128), (4, 64), (8, 32), (16, 16)
  2. (1, 300), (2, 150), (3, 100), (4, 75), (5, 60), (6, 50), (10, 30), (12, 25)
  3. (1, 324), (2, 162), (3, 108), (4, 81), (6, 54), (9, 36), (12, 27), (18, 18)
  4. (1, 400), (2, 200), (4, 100), (5, 80), (8, 50), (10, 40), (16, 25)
  5. (1, 441), (3, 147), (7, 63), (9, 49)
  6. (1, 484), (2, 242), (11, 44)
  7. (1, 576), (2, 288), (3, 192), (4, 144), (6, 96), (8, 72), (9, 64), (12, 48), (16, 36), (24, 24)
  8. (1, 625), (5, 125), (25, 25)
  9. (1, 729), (3, 243), (9, 81), (27, 27)
  10. (1, 800), (2, 400), (4, 200), (5, 160), (8, 100), (10, 80), (16, 50), (20, 40)
  11. (1, 900), (2, 450), (3, 300), (4, 225), (5, 180), (6, 150), (9, 100), (10, 90), (15, 60), (18, 50), (25, 36)
  12. (1, 1024), (2, 512), (4, 256), (8, 128), (16, 64), (32, 32)
  13. (1, 1210), (2, 605), (5, 242)
  14. (1, 1296), (2, 648), (3, 432), (4, 324), (6, 216), (8, 162), (9, 144), (12, 108), (16, 81), (18, 72), (24, 54), (36, 36)
  15. (1, 1440), (2, 720), (3, 480), (4, 360), (5, 288), (6, 240), (8, 180), (9, 160), (10, 144), (12, 120), (15, 96), (16, 90), (18, 80), (20, 72), (24, 60), (30, 48)
  16. (1, 1680), (2, 840), (3, 560), (4, 420), (5, 336), (6, 280), (7, 240), (8, 210), (10, 168), (12, 140), (14, 120), (15, 112), (16, 105), (20, 84), (21, 80), (24, 70), (28, 60), (30, 56), (35, 48)
  17. (1, 1800), (2, 900), (3, 600), (4, 450), (5, 360), (6, 300), (8, 225), (9, 200), (10, 180), (12, 150), (15, 120), (18, 100), (20, 90), (24, 75), (30, 60), (36, 50)
  18. (1, 2000), (2, 1000), (4, 500), (5, 400), (8, 250), (10, 200), (20, 100), (25, 80), (40, 50)
  19. (1, 2200), (2, 1100), (4, 550), (5, 440), (10, 220), (11, 200), (20, 110)
  20. (1, 2400), (2, 1200), (3, 800), (4, 600), (5, 480), (6, 400), (8, 300), (10, 240), (12, 200), (15, 160), (16, 150), (20, 120), (24, 100), (30, 80), (40, 60)

I hope this helps you understand factor pairs better! Keep practising, and you’ll become a factor pair expert in no time!