The number (492-4)(493-49) is divisible by

Question

The number (492-4)(493-49) is divisible by (A) 6! (B) 5! (C) 7! (D) 9!

Tardigrade Admin · Accepted Answer

Given expression = (492 - 22) × 49 (492 - 1) = 51 × 47 × 49 × 50 × 48 = 51 × 50 × 49 × 48 × 47 is the product of five consecutive integers. Hence it is divisible by 5!.

Q. The number $(4 9^{2} - 4) (4 9^{3} - 49)$ is divisible by_______

$6!$

$5!$

$7!$

$9!$

Given expression $= (4 9^{2} - 2^{2}) \times 49 (4 9^{2} - 1)$
$= 51 \times 47 \times 49 \times 50 \times 48$
$= 51 \times 50 \times 49 \times 48 \times 47$
is the product of five consecutive integers. Hence it is divisible by $5!$ .

Q. The number (492−4)(493−49) is divisible by_______

6!

5!

7!

9!