Question

What is the remainder when 8^48 is divided by 63?

(a) 4

(b) 2

(c) 1

(d) 7

I have been asked this question during an internship interview.

My question is based upon Binomial Theorem for Positive Integral Index in division Binomial Theorem of Mathematics – Class 11

Answer 1

Right option is (c) 1

The explanation is: 8^58 can be written as (8^2)^24.

8^48 = (64)^24

8^48 = (63 + 1)^24

We know that (60 + 1)^24 = \(\Sigma_{r = 0}^{r = 24}\)(24Cr 63^24 – r 1^r)

= 24C0 63^24 4^0 + 24C1 63^23 4^1 +….+24C23 63^1 4^23 + 24C24 63^0 1^24

= 63 x k + 1

Therefore, the remainder will be 1.