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| Math Central | Quandaries & Queries |
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Question from Muqadasah, a student: A number, when divided by 136, leaves remainder 36. If the same number is divided by 17, what will be the remainder? |
Muqadasah,
The key to this problem is that 17 divides 136, in fact $136 = 8 \times 17.$
Suppose the number you want is $n$ then there is an integer $k$ so that
\[\frac{n}{136} = k + \frac{36}{136}.\]
You now want to know the remainder when you divide $n$ by $17?$ Write
\[\frac{n}{17}.\]
Multiply the numerator and denominator by 8 and simplify.
Write back if you need more assistance,
Penny
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