Q.1 - Intermediate Algebra

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.

84

Step-by-Step Solution

Answer

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

Step 1. Given information

The given number is 84.

It is to be determined whether 84 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.

84 ends with 4.

Therefore, 84 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 84 is $8+4=12$.

12 is divisible by 3.

Therefore, 84 is divisible by 3.

Step 4. Checking divisibility by 5

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

84 does not end with 0 or 5.

Therefore, 84 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.

84 is divisible by both 2 and 3.

Therefore, 84 is divisible by 6.

Step 6. Checking divisibility by 10

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

84 does not end with 0.

Therefore, 84 is not divisible by 10.

Step 7. Conclusion

Therefore, 84 is divisible by 2, by 3, and by 6.