Competition problem — Number theory

Library / /11 of 20

Number theory Difficulty 4.0 AIME Find the answer South Africa

What is the difference between the largest and the second largest odd factors of $2016$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

$2016$ is $2^5 \times 3^2 \times 7$ . The largest odd factor is $3^2 \times 7 = 63$ ; and the next largest odd factor is $3 \times 7 = 21$ . $63 - 21 = 42$

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.