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$75$ is the remainder of $X$ divided by $132$. What is the remainder of $X$ divided by $12$? I know the answer is $3$ but how do we get that answer?

Empy2
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user175533
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2 Answers2

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If $X=132y+75$, $y$ is integer. Then $X=12*(11y)+6*12+3=12(11y+6)+3$. Therefore the remainder of the division by $12$ is $3$.

Mark Bennet
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Josh Shelley
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Hint: if you have a remainder of $75$ when you devide $X$ by $132$, then this must mean that $X=132q+75$ for some integer $q$.....

Full answer: So we know that $X=132q+75$. Next we wonder what will happen if we devide $X$ by $12$...
Well, we'll get something like this:$$\frac X{12}=\frac{132q+75}{12}=\frac{132q}{12}+\frac{75}{12}$$$132q=12\times11\times q $, so this leaves us with no remainder. $75=12\times6+3$, which leaves us with a remainder of $3$.

So in conclusion $X$ has a remainder of $3$ when devided by $12$.

gebruiker
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  • I appreciate that you are trying to help the OP discover the solution themselves, but in a problem this shallow, a hint that does little beyond restating the Question seems like more of a Comment than an Answer. Why not complete the "..."; it may be of service to future Readers. – hardmath Sep 26 '14 at 15:57