How many pairs of positive integers (m,n) satisfy the equation m x n = 2016?

How many pairs of positive integers (m,n) satisfy the equation m x n = 2016?
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1 Answer

2016=2×2×2×2×2×3×3×7.

From this breakdown into factors we can split 2016 into pairs of factors:

(m,n)=(2,1008), (3,672), (4,504), (6,336), (7,288), (8,252), (9,224), (12,168), (14,144), (16,126), (18,112), (21,96), (24,84), (28,72), (32,63), (36,56), (42,48). There are 17 pairs.

by Top Rated User (1.1m points)

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