Q.4 - 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.

942

Step-by-Step Solution

Answer

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

Step 1. Given information

The given number is 942.

It is to be determined whether 942 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.

942 ends with 2.

Therefore, 942 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 942 is $9+4+2=15$.

15 is divisible by 3.

Therefore, 942 is divisible by 3.

Step 4. Checking divisibility by 5

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

942 does not end with 0 or 5.

Therefore, 942 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.

942 is divisible by both 2 and 3.

Therefore, 942 is divisible by 6.

Step 6. Checking divisibility by 10

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

942 does not end with 0.

Therefore, 942 is not divisible by 10.

Step 7. Conclusion

Therefore, 942 is divisible by 2, by 3 and by 6.