Question

${1400}^n$ is NOT divisible by which of the following, if n is a natural number:

• A. 100
• B. 175
• C. 56
• D. 210

Answer 1

The correct option is D

210

${1400}^n$ =${\left(2^3{5}^{2}7\right)}^n$
For any ‘n’, ${1400}^n$ has factors 8, 25, 7, (25 $\times$ 4 = 100), (25 $\times$ 7 = 175), (7 $\times$ 8 = 56), but 210 = 3 $\times$ 7 $\times$ 10, which can not be structured from the prime factors of 1400.
So this is not divisible by 210.