Is Number Divisible By 3? Quick And Easy Hack

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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)

  1. 483
  2. 2,064
  3. 11,985
  4. 375,423
  5. 7,547,936
  6. 91,056,437
  7. 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:

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

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