Question

The number $(49^2-4)(49^2-49)$ is divisible by ..................

• A. 6!
• B. 5!
• C. 7!
• D. 9!

Answer 1

Answer: (B)

Given, $\left(49^2-4\right)\left(49^3-49\right)$
$=\left[(49{)}^2-(2{)}^2\right]\left[(49{)}^2-1\right]\cdot 49$
$=(49+2)(49-2)(49+1)(49-1)\cdot 49$
$=51\cdot 47\cdot 50\cdot 48\cdot 49$
$=(51\cdot 50\cdot 49\cdot 48\cdot 47)$
Which is the product of five consecutive integers and hence it divisible by $5!$.