Library / /56 of 165

, 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) $4$

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.