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# Number Theory

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N is a positive integer. When N is divided by 3, the remainder is 2. When N is divided by 4, the remainder is 2. What is the remainder when N is divided by 12?

Nov 14, 2022

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The remainder is 8.

Nov 14, 2022
#2
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The number N has a remainder of 2 when divided by 3 and 4, so the number will have a remainder of 2 when divided by $$3\cdot 4 = 12$$. Thus, N is of the form $$N = 12x+2$$. This easily shows that the remainder when N is divided by 12 is $$\boxed{2}$$ .

Hope this helped :P

Nov 14, 2022