Without dividing, determine if 78,510 is divisible by 6 and explain how you know.

To determine if the number 78,510 is divisible by 6, we need to check if it meets the criteria for divisibility by both 2 and 3, since a number is divisible by 6 if and only if it is divisible by both of these numbers. 1. **Divisibility by 2**: A number is divisible by 2 if its last digit is even. The last digit of 78,510 is 0, which is even. Therefore, 78,510 is divisible by 2. 2. **Divisibility by 3**: A number is divisible by 3 if the sum of its digits is divisible by 3. Let's calculate the sum of the digits of 78,510: - 7 + 8 + 5 + 1 + 0 = 21 Now, we check if 21 is divisible by 3. The sum of the digits of 21 is: - 2 + 1 = 3 Since 3 is divisible by 3, we conclude that 21 is also divisible by 3. Therefore, 78,510 is divisible by 3. Since 78,510 is divisible by both 2 and 3, we can conclude that it is also divisible by 6. Thus, **78,510 is divisible by 6**.