A number when divided by 899 gives a remainder 63. The remainder when this number is divided by 29 is?

Question

Am I supposed to try division algorithm . I don't know what to do at all . Plz help

Answer 1

Consider the number be $a$. By assumption, we have $$a=899q+63.$$

Noting that $899=29\times 31$, we have $$a=29(31q)+63=29(31q)+2\times 29+5$$ so, $$a=29(31q+2)+5$$ thus the remainder is $5$.

Answer 2

Here the key is that $29 | 899$ so we can write:

$$n=899k+63$$

Where $n$ is our number.

$$n=29(31k)+63$$ $$n=29(31k)+29\times 2 +5$$ $$n=29(31k+2)+5$$ $$n\equiv 5 \pmod{29}$$

:)