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

1. 5
2. 6
3. 7
4. 4

Explanation

Explanation:
To determine if a number is divisible by 132, we need to check if it’s divisible by both 4 and 33 because 132 is the product of 4 and 33.
First, we check divisibility by 4: A number is divisible by 4 if its last two digits form a number that is divisible by 4.
Then, we check divisibility by 33: A number is divisible by 33 if the sum of its digits is divisible by 3 and the number formed by its last two digits is divisible by 11.
Let’s check each of the given numbers:
264: Divisible by 4 (last two digits are 64) and 33 (sum of digits = 2 + 6 + 4 = 12, which is divisible by 3, and 64 is divisible by 11).
396: Divisible by 4 (last two digits are 96) and 33 (sum of digits = 3 + 9 + 6 = 18, which is divisible by 3, and 96 is divisible by 11).
462: Divisible by 4 (last two digits are 62) and 33 (sum of digits = 4 + 6 + 2 = 12, which is divisible by 3, and 62 is not divisible by 11).
792: Divisible by 4 (last two digits are 92) and 33 (sum of digits = 7 + 9 + 2 = 18, which is divisible by 3, and 92 is not divisible by 11).
968: Divisible by 4 (last two digits are 68) and 33 (sum of digits = 9 + 6 + 8 = 23, which is not divisible by 3).
2178: Not divisible by 4 (last two digits are 78).
5184: Divisible by 4 (last two digits are 84) and 33 (sum of digits = 5 + 1 + 8 + 4 = 18, which is divisible by 3, and 84 is divisible by 11).
6336: Divisible by 4 (last two digits are 36) and 33 (sum of digits = 6 + 3 + 3 + 6 = 18, which is divisible by 3, and 36 is divisible by 11).
Out of the given numbers, 264, 396, 5184, and 6336 are divisible by 132. So, there are 4 numbers divisible by 132.