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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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