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UKMT Intermediate Mathematical Challenge, 2016

Number theory Difficulty 1.0 Junior Find the answer United Kingdom

How many of the following positive integers are divisible by 24? $2^2 \times 3^2 \times 5^2 \times 7^3$ , $2^2 \times 3^2 \times 5^3 \times 7^2$ , $2^2 \times 3^3 \times 5^2 \times 7^2$ , $2^3 \times 3^2 \times 5^2 \times 7^2$

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $4$

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