Competition problem — Number theory

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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. Fractions can be typed as 3/2, and spacing doesn't matter.

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 $3 \times 7 = 21$ . $63 - 21 = 42$

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