Which of the following numbers is divisible by 6?

Which of the following numbers is divisible by 6?

• A. 12345
• B. 12960
• C. 7890
• D. 10101

Answer: (B)

To determine if a number is divisible by 6, it must satisfy two conditions: it must be divisible by both 2 and 3. For divisibility by 2, a number must be even, which means it should end with 0, 2, 4, 6, or 8. In the case of the number 12960, it ends with a 0, indicating that it is even and therefore divisible by 2. For divisibility by 3, the sum of the digits in the number must be divisible by 3. For 12960, the sum of the digits is 1 + 2 + 9 + 6 + 0 = 18. Since 18 is divisible by 3, this confirms that 12960 meets the second condition for divisibility by 6. Combining both of these criteria, 12960 is divisible by both 2 and 3, making it divisible by 6.

To determine if a number is divisible by 6, it must satisfy two conditions: it must be divisible by both 2 and 3.

For divisibility by 2, a number must be even, which means it should end with 0, 2, 4, 6, or 8. In the case of the number 12960, it ends with a 0, indicating that it is even and therefore divisible by 2.

For divisibility by 3, the sum of the digits in the number must be divisible by 3. For 12960, the sum of the digits is 1 + 2 + 9 + 6 + 0 = 18. Since 18 is divisible by 3, this confirms that 12960 meets the second condition for divisibility by 6.

Combining both of these criteria, 12960 is divisible by both 2 and 3, making it divisible by 6.