How do you know if a number is divisible by three?

The fastest way of determine if a number can be divisible by 3 is to add up all the digits in the number and if that number is divisible by 3 then the original number is divisible by 3.

For example, suppose the original number tested to see if it can be divisible by 3 is the number 1,234.

To calculate the sum of all the digits in this number you would add each number seen: 1 + 2 + 3 + 4 = 10

As 10 is not divisible by 3 the original number 1,234 is also not divisible by 3.

## Faster Check

If you find there are too many numbers to add up then you could speed up your sum of all the digits by excluding a certain set of numbers.

To make your count even faster exclude the digits 3, 6, 9 and 0 from the original number.

For example, if the original number is 1,363,999 then by knocking out the 3’s, 6’s and 9’s you would be left with the number 1.

As 1 is not divisible by 3 the original number is not divisible by 3.

Easy!

## Even Faster?

Try pairing numbers up that add up to a multiple of 3 (3, 6, 9, 12, 15) and cross them off if they do.

For example, suppose the original number is 34,853,631.

- The first digit 3 you can cross off as it’s divisible by 3;
- The next 2 digits 4 and 8 you can cross off as they sum to 12 which is a multiple of 3;
- Strike out the 3, 6 and 3.
- All that’s left is 5 and 1 which add up to 6 – another multiple of 3.

Can you see how after doing this a few times you can get really fast at finding out if a number is divisible by three?

## Are These Numbers Divisible By 3?

Test your newfound knowledge on the following set of numbers to see if you have grasped the concept, and then check your answers below:

(Time yourself and see how long it takes)

- 483
- 2,064
- 11,985
- 375,423
- 7,547,936
- 91,056,437
- 295,743,689

How did you go?

Here are the answers for each number above I’ve struck out the 0, 3, 6 and 9’s from the original number:

- Yes. 4 + 8 = 12
- Yes. 2 + 4 = 6
- Yes. 1 + 8 = 9 & 1 + 5 = 6
- Yes. 7 + 5 = 12 & 4 + 2 = 6
- No. 7 + 5 = 12 & 7 + 6 = 13
- No. 1 + 5 = 6 & 4 + 7 = 11
- No. 2 + 4 = 6, 5 + 7 = 12 & 8

How did you go?

## Summary

To determine if a number is divisible by 3 fast remove all the 0, 3, 6 and 9 digits then add up all the remaining digits. If this number is divisible by 3 then the original number is divisible by 3 too.

Next you might want to explore how to easily determine if a number is divisible by 4 .