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Year 8 Maths — Playing with numbers

Use the divisibility tests and letter-for-digit puzzles to find missing digits.

Name: ________________________

  1. 1.5*7 is divisible by 3. What is the largest digit that can replace the star?

  2. 2.Put these numbers in order by how many of 2, 3, 5 and 9 divide into them exactly, fewest first.

    • 15
    • 7
    • 18
    • 90
    • 4

  3. 3.A two-digit number is 27 more than the number you get by reversing its digits, and its two digits add to 11. What is the number?

  4. 4.Match each divisibility test to the number it tests for.

    • The last digit is 0 or 5
    • The digits add to a multiple of 3
    • The last two digits make a multiple of 4
    • The digits add to a multiple of 9
    • The last digit is even
    • 3
    • 4
    • 2
    • 9
    • 5

  5. 5.In the sum A7 + 4A = 113, the letter A stands for one digit. What digit is A?

  6. 6.What is the smallest digit that can replace the star so that 3*5 is divisible by 3?

  7. 7.How can you tell that 4832 is divisible by 8 without dividing the whole number?

    • a) Its digits add to a multiple of 8
    • b) Its first digit is divisible by 8
    • c) It ends in an even digit
    • d) Its last three digits, 832, make a multiple of 8

  8. 8.What digit must replace the star so that 21*8 is divisible by 9?

Answer key — Year 8 Maths — Playing with numbers

  1. 1. 9
  2. 2. 1. 7 2. 4 3. 15 4. 18 5. 90
  3. 3. 74
  4. 4. The last digit is 0 or 5 → 5; The digits add to a multiple of 3 → 3; The last two digits make a multiple of 4 → 4; The digits add to a multiple of 9 → 9; The last digit is even → 2
  5. 5. 6
  6. 6. 1
  7. 7. d) Its last three digits, 832, make a multiple of 8
  8. 8. 7