CBSE Class 10 Answered

Dear student,

Let the number be N.

According to the question, when divided by 88, it leaves 8 as remainder.

=> N = 88q + 8    (where q is some integer quotient)

=> N = 8x11xq + 8

=> N = 8(11q + 1)

Now, when divided by 11, the remainder will be the product of remainders left by individual divisions of the two factors, 8 and (11q-1).

Remainder left by 8 when divided by 11 = 8

Remainder left by (11q+1) when divided by 11 = 1

=> Remainder left by N=8(11q+1) when divided by 11 = 8 x 1 = 8.

Therefore the number N leaves remainder 8 when divided by 11.

Regards Topperlearning.