Q.6 - 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.

39,075

Step-by-Step Solution

Answer

39,075 is divisible by 3 and by 5.

Step 1. Given information

The given number is 39,075.

It is to be determined whether 39,075 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.

39,075 ends with 5.

Therefore, 39,075 is not 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 39,075 is $3+9+0+7+5=24$.

24 is divisible by 3.

Therefore, 39,075 is divisible by 3.

Step 4. Checking divisibility by 5

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

39,075 ends with 5.

Therefore, 39,075 is divisible by 5.

Step 5. Checking divisibility by 6

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

39,075 is divisible by 3 but not by 2.

Therefore, 39,075 is not divisible by 6.

Step 6. Checking divisibility by 10

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

39,075 does not end with 0.

Therefore, 39,075 is not divisible by 10.

Step 7. Conclusion

Therefore, 39,075 is divisible by 3 and by 5.