How many of the following numbers are divisible by 132?264, 396, 462,

1.	How many of the following numbers are divisible by 132?264, 396, 462, 792, 968, 2178, 5184, 63361. 42. 53. 64. 7
Answer» Correct Answer - Option 1 : 4 Calculation: 132 = 3 × 4 × 11. 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. Here 3, 4 and 11 are pair-wise co-prime numbers. If a number is not divisible by 3 or 4 or 11, then it is not divisible by 132. ⇒ 264 is divisible by 3, 4 and 11; so 264 is divisible by 132. ⇒ 396 is divisible by 3, 4 and 11; so 396 is divisible by 132. ⇒ 462 is divisible by 3 and 11 but not divisible by 4; so 462 is not divisible by 132. ⇒ 792 is divisible by 3, 4 and 11; so 792 is divisible by 132. ⇒ 968 is divisible by 4 and 11 but not divisible by 3; so 462 is not divisible by 132. ⇒ 2178 is divisible by 3 and 11 but not divisible by 4; so 462 is not divisible by 132. ⇒ 5184 is divisible by 3 and 4 but not divisible by 11; so 462 is not divisible by 132. ⇒ 6336 is divisible by 3, 4 and 11; so 6336 is divisible by 132. Only 264, 396, 792 and 6336 are divisible by 132. ∴ 4 numbers are divisible by 132.

How many of the following numbers are divisible by 132?264, 396, 462, 792, 968, 2178, 5184, 63361. 42. 53. 64. 7

Answer» Correct Answer - Option 1 : 4

Calculation:

132 = 3 × 4 × 11.

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.

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

If a number is not divisible by 3 or 4 or 11, then it is not divisible by 132.

⇒ 264 is divisible by 3, 4 and 11; so 264 is divisible by 132.

⇒ 396 is divisible by 3, 4 and 11; so 396 is divisible by 132.

⇒ 462 is divisible by 3 and 11 but not divisible by 4; so 462 is not divisible by 132.

⇒ 792 is divisible by 3, 4 and 11; so 792 is divisible by 132.

⇒ 968 is divisible by 4 and 11 but not divisible by 3; so 462 is not divisible by 132.

⇒ 2178 is divisible by 3 and 11 but not divisible by 4; so 462 is not divisible by 132.

⇒ 5184 is divisible by 3 and 4 but not divisible by 11; so 462 is not divisible by 132.

⇒ 6336 is divisible by 3, 4 and 11; so 6336 is divisible by 132.

Only 264, 396, 792 and 6336 are divisible by 132.

∴ 4 numbers are divisible by 132.