An easy question on divisibility and factors for P4–P5, with a step-by-step solution, diagrams and the answer. Common in the Hua Xia Cup's P4 and P5 qualifying rounds and finals; harder ones use how many factors a number has, and square numbers.
The question
Ming and his classmates play a clapping game: they count in turn from 1 up to 35.
Whenever the number is a multiple of 3, they clap once instead of saying it.
Counting from 1 to 35, how many claps are there?
Show the hints (2)
💡Hint 1: A multiple of 3 is 3 times some number, and 3 times n is the nth multiple. The last multiple not above 35 is 3 times what?
💡Hint 2: How many 3s fit into 35?
Worked solution
Have a go first, then read the solution step by step.
1.The clapping numbers: 3 × 1, 3 × 2, … up to 35.
2.35 ÷ 3 = 11 remainder 2, so the last one is 3 × 11 = 33.
3.11 claps in all.
⚠️Common mistake: counting the leftover 2 as one more clap and answering 12.
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