Question

In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.

96

Short answer

96 is divisible by 2, by 3, and by 6.

Step-by-step solution

Step 1. Given information

The given number is 96.

It is to be determined whether 96 is divisible by 2, by 3, by 5, by 6, and by 10.

Step 2. Checking divisibility by 2

A number is divisible by 2 if the last digit is 0, 2, 4, 6, or 8.

96 ends with 6.

Therefore, 96 is divisible by 2.

Step 3. Checking divisibility by 3

A number is divisible by 3 if the sum of digits is divisible by 3.

The sum of the digits of 96 is $9+6=15$.

15 is divisible by 3.

Therefore, 96 is divisible by 3.

Step 4. Checking divisibility by 5

A number is divisible by 5 if the last digit is 0, or 5.

96 does not end with 0 or 5.

Therefore, 96 is not divisible by 5.

Step 5. Checking divisibility by 6

A number is divisible by 6, if it is divisible by both 2 and 3.

96 is divisible by both 2 and 3.

Therefore, 96 is divisible by 6.

Step 6. Checking divisibility by 10

A number is divisible by 10 if the last digit is 0.

96 does not end with 0.

Therefore, 96 is not divisible by 10.

Step 7. Conclusion

Therefore, 96 is divisible by 2, by 3, and by 6.