Factors, multiples, squares and cubes (age 9+) · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Using factors, multiples, and squares to solve problems

Mathematics · Multiplication & Division · ages 9-10
Name ______________________   Date ____________

  1. What is the smallest multiple of 6 that is greater than 50?

    Answer: ______________

  2. Is 156 a multiple of 6?

    • Yes, 6 x 25 = 156
    • No, 156 is odd
    • Yes, 6 x 26 = 156
    • No, 6 x 24 = 156

  3. Which number is definitely a multiple of 6?

    • 44
    • 51
    • 48

  4. Breaking 24 × 25 into 6 × (4 × 25) makes the multiplication easier to solve.

    Circle one:   True   False

  5. Which method uses factor pairs to make 12 × 15 easier to work out?

    • Break 12 into 4 × 3, so do 15 × 4 = 60, then 60 × 3 = 180
    • Add 12 and 15 to get 27
    • Multiply 12 × 15 straight down without breaking it apart

  6. Which of these numbers is prime?

    • 15
    • 21
    • 27
    • 13

  7. Which two square numbers add to make 100?

    • 64 and 36
    • 49 and 49
    • 64 and 25
    • 81 and 9

  8. 342 is even, and its digits add to 9. Is 342 a multiple of 6?

    • Yes, because it's even and the digit sum (9) is a multiple of 3
    • No, because 9 is not a multiple of 3
    • No, because 342 is an odd number

  9. Ben says 91 is a multiple of 6 because 9 + 1 = 10 is close to a multiple of 3. What is wrong with his reasoning?

    • 10 is not a multiple of 3, and 91 is odd too, so it fails both checks for being a multiple of 6
    • Ben is right, 91 is a multiple of 6
    • 91 is even, so it must be a multiple of 6

  10. What is the 7th multiple of 9?

    Answer: ______________

LightMySky · lightmysky.comW1-mt_0Wg5F97osg-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Using factors, multiples, and squares to solve problems W1-mt_0Wg5F97osg-s1

  1. 54 · Multiples of 6 near 50 are 48 and 54, so the smallest one above 50 is 54.
  2. Yes, 6 x 26 = 156 · 156 is a multiple of 6 because 6 x 26 = 156 with nothing left over.
  3. 48 · 48 is even and its digits add to 12, a multiple of 3, so it passes both tests for being a multiple of 6.
  4. True · 24 = 6 × 4, so 6 × (4 × 25) = 6 × 100 = 600, which is much easier than multiplying 24 × 25 directly.
  5. Break 12 into 4 × 3, so do 15 × 4 = 60, then 60 × 3 = 180 · Splitting 12 into 4 × 3 turns one hard multiplication into two easy ones: 15 × 4 = 60, then 60 × 3 = 180.
  6. 13 · 13 is prime because its only factors are 1 and 13. Each other choice has extra factors.
  7. 64 and 36 · 64 + 36 = 100, and both 64 (8 x 8) and 36 (6 x 6) are square numbers.
  8. Yes, because it's even and the digit sum (9) is a multiple of 3 · 342 passes both checks: it is even, and 9 is a multiple of 3. So it is a multiple of 6.
  9. 10 is not a multiple of 3, and 91 is odd too, so it fails both checks for being a multiple of 6 · 91 is odd, and its digit sum (10) is not a multiple of 3. It fails both tests, so it is not a multiple of 6.
  10. 63 · The 7th multiple of 9 is 7 x 9 = 63.
Worksheet · LightMySky