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.

896

Short answer

896 is divisible by 2.

Step-by-step solution

Step 1. Given information

The given number is 896.

It is to be determined whether 896 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.

896 ends with 6.

Therefore, 896 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 896 is $8+9+6=23$.

23 is not divisible by 3.

Therefore, 896 is not divisible by 3.

Step 4. Checking divisibility by 5

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

896 does not end with 0 or 5.

Therefore, 896 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.

896 is divisible by 2 but not by 3.

Therefore, 896 is not divisible by 6.

Step 6. Checking divisibility by 10

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

896 does not end with 0.

Therefore, 896 is not divisible by 10.

Step 7. Conclusion

Therefore, 896 is divisible by 2.