## Divisibility

The capability regarding a whole number to be divided by another whole number with no remainder is referred to as divisibility. Quite often, it is beneficial to determine if whole numbers are divisible by 2, 3, 5, or 10. Consequently, various rules may be used to quickly determine visibility without actually performing division:

- A whole number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8
- A whole number is divisible by 3 if the sum of its digits are divisible by 3
- A whole number is divisible by 5 if its last digit is either 0 or 5
- A whole number is divisible by 10 if its last digit is 0

Example:

Is 195 divisible by 2, 3, 5, and/or 10?

Solution:

- As the last digit of 195 is not 0, 2, 4, 6 or 8, 195 is not divisible by 2.
- As the sum of digits (1 + 9 + 5 = 15) equals 15, which is divisible by 3, 195 is divisible by 3.
- As the last digit of 195 is five, 195 is divisible by 5.
- As the last digit of 195 does not end in zero, 195 is not divisible by 10.