Let N = 1421 * 1423 * 1425. What is the remainder when N is divided by 12?

Solution

The numbers 1421, 1423 and 1425 when divided by 12 give remainder 5, 7 and 9 respectively.

5*7*9 mod 12 = 11 * 9 mod 12 = 99 mod 12 = 3

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