Is 1800 divisible by 9 and 3?

Answer 1

1800 / 9 = 200

1800 / 3 = 600

Therefore, the answer is, yes.

Instead of doing the actual division, the number can be tested for divisibility:

* by 9:

add the digits together and if this sum is divisible by 9, then so is the original number.

The test can be repeated on the sum, so if the summing is repeated until a single digit remains, if this digit is 9, then the original number is divisible by 9; otherwise, this single digit is the remainder when the original number is divided by 9. (This single digit is also known as the digital root of the number.)

* by 3:

add the digits together and if this sum is divisible by 3, then so is the original number.

The test can be repeated on the sum, so if the summing is repeated until a single digit remains, if this digit is divisible by 3 (ie is one of 3, 6 or 9), then the original number is divisible by 9.

For 1800: 1 + 8 + 0 + 0 = 9

This is 9, so the original number (1800) is divisible by 9;

This is 9 which is one of 3, 6 or 9, so the original number (1800) is divisible by 3.

Note: as 9 = 3 × 3, all numbers divisible by 9 are automatically also divisible by 3.