Q.5 - 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.

22,335

Step-by-Step Solution

Answer

22,335 is divisible by 3 and by 5.

Step 1. Given information

The given number is 22,335.

It is to be determined whether 22,335 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.

22,335 ends with 5.

Therefore, 22,335 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 22,335 is $2+2+3+3+5=15$.

15 is divisible by 3.

Therefore, 22,335 is divisible by 3.

Step 4. Checking divisibility by 5

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

22,335 ends with 5.

Therefore, 22,335 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.

22,335 is divisible by 3 but not by 2.

Therefore, 22,335 is not divisible by 6.

Step 6. Checking divisibility by 10

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

22,335 does not end with 0.

Therefore, 22,335 is not divisible by 10.

Step 7. Conclusion

Therefore, 22,335 is divisible by 3 and by 5.