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Ignition Learning — Activity Sheet

Factors, multiples & primes

Mathematics · Year 7

Name: ______________________Date: ____________

A factor of a number divides into it evenly with nothing left over — the factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is what you get by multiplying a number by a whole number — multiples of 4 are 4, 8, 12, 16... A prime number has exactly two factors, 1 and itself (2, 3, 5, 7, 11...); a number with more factors than that is composite.

Example

You want to split 24 lollies evenly among your friends with none left over. The number of friends must be a factor of 24 — so 1, 2, 3, 4, 6, 8, 12 or 24 friends would work evenly, but 5 friends would not (24 ÷ 5 leaves a remainder).

Key terms

Factor:
A number that divides evenly into another number.
Multiple:
The result of multiplying a number by a whole number.
Prime number:
A number with exactly two factors: 1 and itself.

Questions

  1. 1. Which is a factor of 12?

    • 5
    • 4
    • 7
    • 9

  2. 2. Which is a multiple of 4?

    • 6
    • 10
    • 12
    • 15

  3. 3. Is 7 a prime number?

    • Yes
    • No
    • Only sometimes
    • Cannot tell

  4. 4. What are the factors of 6?

    • 1, 2, 3, 6
    • 1, 6 only
    • 2, 3 only
    • 1, 2, 3, 4, 6

  5. 5. The first three multiples of 5 are:

    • 5, 10, 15
    • 1, 5, 10
    • 5, 6, 7
    • 0, 5, 10

  6. 6. Which of these is NOT a prime number?

    • 2
    • 3
    • 4
    • 5

  7. 7. How many friends can share 10 lollies evenly (more than 1 each, no leftovers)?

    • 2 or 5
    • 3 or 4
    • 6 or 7
    • 8 or 9

  8. 8. What are all the factors of 18?

    • 1, 2, 3, 6, 9, 18
    • 1, 3, 6, 18
    • 2, 3, 6, 9
    • 1, 2, 9, 18

  9. 9. What is the highest common factor (HCF) of 8 and 12?

    • 2
    • 4
    • 6
    • 24

  10. 10. What is the lowest common multiple (LCM) of 3 and 4?

    • 7
    • 12
    • 24
    • 1

  11. 11. You want to split 20 apples between friends evenly, more than 2 each, no leftovers. How many friends could there be?

    • 3
    • 4
    • 7
    • 9

  12. 12. Which number is both a factor of 20 and a multiple of 5?

    • 2
    • 10
    • 3
    • 7

  13. 13. How many prime numbers are there between 1 and 10?

    • 2
    • 3
    • 4
    • 5

  14. 14. A composite number is one that:

    • Has only 2 factors
    • Has more than 2 factors
    • Is always even
    • Is always prime

  15. 15. Two buses leave the depot together. One returns every 6 minutes, the other every 8 minutes. After how many minutes will they next leave together?

    • 14
    • 24
    • 48
    • 6

  16. 16. What is the HCF of 18 and 24?

    • 3
    • 6
    • 9
    • 12

  17. 17. A school wants to arrange 36 chairs into equal rows with more than 4 rows and more than 4 chairs per row. Which arrangement works?

    • 6 rows of 6
    • 2 rows of 18
    • 36 rows of 1
    • 3 rows of 12

  18. 18. Which number is prime?

    • 21
    • 27
    • 29
    • 33

  19. 19. What is the LCM of 6 and 9?

    • 15
    • 18
    • 54
    • 3

  20. 20. A ribbon-cutting machine cuts a ribbon into equal pieces with no leftovers, for ribbons that are multiples of 7cm. Which ribbon length would NOT work evenly into 7cm pieces?

    • 35cm
    • 42cm
    • 50cm
    • 49cm

  21. 21. What are all the common factors of 16 and 24?

    • 1, 2, 4, 8
    • 1, 2, 3, 4
    • 2, 4, 6, 8
    • 1, 4, 6, 8

Answer key (parent copy)

  1. 1. 4
  2. 2. 12
  3. 3. Yes
  4. 4. 1, 2, 3, 6
  5. 5. 5, 10, 15
  6. 6. 4
  7. 7. 2 or 5
  8. 8. 1, 2, 3, 6, 9, 18
  9. 9. 4
  10. 10. 12
  11. 11. 4
  12. 12. 10
  13. 13. 4
  14. 14. Has more than 2 factors
  15. 15. 24
  16. 16. 6
  17. 17. 6 rows of 6
  18. 18. 29
  19. 19. 18
  20. 20. 50cm
  21. 21. 1, 2, 4, 8