Question

Which of these numbers is divisible by 132?

• A. 1,17,085
• B. 1,91,044
• C. 2,11,804
• D. 1,03,620

Answer 1

The Correct Option is D

Divisibility Check for 132 

- To check if a number is divisible by 132, we need to check its divisibility by both 4 and 33.

Step 1: Divisibility by 4
- A number is divisible by 4 if the last two digits are divisible by 4.

- For 1,03,620, the last two digits are 20. Since:

\[ 20 \div 4 = 5 \]

The number is divisible by 4.

Step 2: Divisibility by 33
- A number is divisible by 33 if:

• The sum of its digits is divisible by 3.
• The alternating sum of its digits is divisible by 11.

 

- The sum of the digits is:

\[ 1 + 0 + 3 + 6 + 2 + 0 = 12 \]

Since \( 12 \div 3 = 4 \), it is divisible by 3.

- The alternating sum of the digits is:

\[ 1 - 0 + 3 - 6 + 2 - 0 = 0 \]

Since \( 0 \div 11 = 0 \), it is divisible by 11.

- Since the number is divisible by both 4 and 33, it is divisible by 132.

Conclusion: The correct answer is (d) 1,03,620.