A number $N$ when divided by 9 leaves the remainder of 5.

Find the remainder when the same number $N$ is divided by 3.

0
1
2

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Using Euclid's division lemma

$N = 9m + 5 \\ N = 3\times 3m + 5 \\ N = 3\times3m + 3 + 2 \\ N = 3(3m+1) + 2 \\ N = 3q+2\text{ (q = 3m+1)} \\ \therefore \fbox{ The remainder is 2 }$