# Divisibility Rule for 3

As a student, many times you might have felt very difficult to divide large numbers by 3. Then why don't you look into the simple trick that can easily check any large number whether it is divisible by 3 or not. Then that trick we call as divisibility rule of 3. This rule will help you to divide any large number with 3. It will be easy for you, in your assignments, exams, and aptitude tests. In this article, we are going to provide you with many things along with the divisibility rule. Check it out now!!

## What is the Divisibility Rule for 3?

The divisivility rule of 3 states that if the sum of the digits of the given whole number is divisible by 3 then the whole number is divisible by 3. For small numbers, you can easily divide by 3 but for large numbers, as it is time taking process you can easily use the divisibility rule for 3.

### Proof of Divisible by 3 Rule

Here we are going to provide you with the proof that you can easily check the number of any type whether it is divisible by 3 or not.

Consider the number 28273637

As per the divisibility rule, you need to sum all the digits of the whole number.

2827= 2+8+2+7 = 19

As 19 is not divisible by 3 the number is not divisible by 3.

(Or)

2827 = 2 × 1000 + 8 × 100 + 2 × 10 + 7 × 1

= 2 × (999 + 1) + 8 × (99 + 1) + 2 × (9 + 1) + 7 × 1

= (2 × 999 + 8 × 99 + 2 × 9) + (2 × 1 + 8 × 1 + 2 × 1 + 7 × 1)

= (2 × 999 + 8 × 99 + 2 × 9) + (2 + 8 + 2 + 7)

As We know that 9, 99, 999,… are divisible by 3, and then the multiples of these numbers are also divisible by 3.

So, the divisibility of 4368 is now dependent on the sum 2 + 8 + 2 + 7.

Here, 2,8,2,7 are the digits of the number 2827.

From the above, the sum of these digits is not divisible by 3 and the whole number is also not divisible by 3.

### What numbers are divisible by 3

List of Numbers divisible by 3: The Numbers 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93, 96, 99, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 150, 153, 156, 159, 162, 165, 168, 171, 174, 177, 180, 183, 186, 189, 192, 195, 198, 201, 204, 207, 210, 213, 216, 219, 222, 225, 228, 231, 234, 237, 240, 243, 246, 249, 252, 255, 258, 261, 264, 267, 270, 273, 276, 279, 282, 285, 288, 291, 294, 297, 300, etc. are divisible by 3.

### FAQs on Test of Divisibility by 3

1. Why does the divisibility rule of 3 work?

The divisible rule of 3 works because 999999… are all divisible by 3.

2. How to prove the divisibility rule for 3?

You can prove the divisibility rule of 3 by some example, take the number 34284,

According to the divisibility rule of 3, add all the digits 3+4+2+8+4 = 21 is divisible by 3. So the number is divisible by 3.

3. What is the divisibility test of 3?

The number is divisible by 3 if the sum of all the digits of that number is divisible by 3.

### Summary

We as a team hope that the information that was given on the divisibility rule for 3 is beneficial for you to check whether the whole number which is large will be divisible by 3 or not. You can also check other divisibility rules for 4,5,6, and for many. Stay connected with our site for more articles, calculators, and many more.