Question

How many of the following numbers are divisible by $132$?
$264,396,462,792,968,2178,5184,6336$

• A. $6$
• B. $4$
• C. $5$
• D. $8$

Answer 1

Answer: (B)

$4$

$\Rightarrow$ Here 3, 4 and 11 are pair wise co-prime numbers.

$\Rightarrow$ $132=3\times 4\times 11$. Also 3,4 and 11 are factors of 132. Hence if a number is divisible by 3, 4 and 11, the number will be divisible by their product 132 also.

$\Rightarrow$ If a number is not divisible by 3 or 4 or 11, it is not divisible by 132.

$\Rightarrow$ 264 is divisible by 3, 4 and 11; So, 264 is divisible by 132

$\Rightarrow$ 396 is divisible by 3, 4 and 11; So, 396 is divisible by 132

$\Rightarrow$ 462 is divisible by 3 and 11, but not divisible by 4; So, 462 is not divisible by 132

$\Rightarrow$ 792 is divisible by 3, 4 and 11; So, 792 is divisible by 132

$\Rightarrow$ 968 is divisible by 4 and 11, but not divisible by 3; So, 968 is not divisible by 132

$\Rightarrow$ 2178 is divisible by 3 and 11, but not divisible by 4; So, 2178 is not divisible by 132

$\Rightarrow$ 5184 is divisible by 3 and 4, but not divisible by 11; So, 5184 is not divisible by 132

$\Rightarrow$ 6336 is divisible by 3, 4 and 11; So, 6336 is divisible by 132

$\Rightarrow$ Hence, only 264, 396 ,792 and 6336 are divisible by 132. So the answer is $4$.