Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Which of these is divisible by 5?
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205 ends in 5.
2 For 4 725: give the digit sum, then 4 725 ÷ 9.
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4 + 7 + 2 + 5 = 18, so 9 divides it: 4 725 ÷ 9 = 525.
3 What is the smallest number greater than 100 that is divisible by both 2 and 5?
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The first multiple of 10 after 100 is 110.
Level 2 · Core
4 Which of these is not divisible by 4?
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34 ÷ 4 leaves a remainder, so 534 is not divisible by 4. 16, 28, 12 and 20 all are.
5 The number 3□6 is divisible by 9. Give the smallest and the largest digit that could be in the box.
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9 + □ is a multiple of 9 when □ = 0 (306 = 9 × 34) or □ = 9 (396 = 9 × 44).
6 What is the largest three-digit number that is divisible by 8?
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8 × 125 = 1 000, so 8 × 124 = 992.
Level 3 · Challenge
7 Three statements are made about 2 316.1 2 316 is divisible by 4.
2 2 316 is divisible by 8.
3 2 316 is divisible by 3.
Which statements are correct?
2 2 316 is divisible by 8.
3 2 316 is divisible by 3.
Which statements are correct?
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16 divides by 4 (1 ✓). 316 ÷ 8 = 39.5 (2 ✗). 2 + 3 + 1 + 6 = 12 (3 ✓). 1 and 3.
8 The five-digit number 42□78 is divisible by 9. What digit is in the box, and what are its last two digits?
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21 + □ = 27 needs □ = 6. The number is 42 678, ending in 78 — not divisible by 4, since 78 is not.
9 How many multiples of 9 are there between 100 and 200?
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108, 117, … , 198: (198 − 108) ÷ 9 + 1 = 11.