# Divisible by 3

A number is divisible by 3, if the sum of its all digits is a multiple of 3 or divisibility by 3.

Consider the multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, .........

 Number Sum of the Digits 121518212427 1 + 2 = 31 + 5 = 61 + 8 = 92 + 1 = 32 + 4 = 62 + 7 = 9

In each case the sum of the digits is divisible by 3.

A number is divisible by 3 if the sum of its digits is divisible by 3.

1. Let us consider the following numbers to find whether the numbers are divisible or not divisible by 3:

(i) 54

Sum of all the digits of 54 = 5 + 4 = 9, which is divisible by 3.

Hence, 54 is divisible by 3.

(ii) 73

Sum of all the digits of 73 = 7 + 3 = 10, which is not divisible by 3.

Hence, 73 is not divisible by 3.

(iii) 137

Sum of all the digits of 137 = 1 + 3 + 7 = 11, which is not divisible by 3.

Hence, 137 is not divisible by 3.

(iv) 231

Sum of all the digits of 231 = 2 + 3 + 1 = 6, which is divisible by 3.

Hence, 231 is divisible by 3.

(v) 194

Sum of all the digits of 194 = 1 + 9 + 4 = 14, which is not divisible by 3.

Hence, 194 is not divisible by 3.

(vi) 153

Sum of all the digits of 153 = 1 + 5 + 3 = 9, which is divisible by 3.

Hence, 54 is divisible by 3.

(vii) 171

Sum of all the digits of 171 = 1 + 7 + 1 = 9, which is divisible by 3.

Hence, 171 is divisible by 3.

(viii) 277

Sum of all the digits of 277 = 2 + 7 + 7 = 16, which is not divisible by 3.

Hence, 277 is not divisible by 3.

(ix) 276

Sum of all the digits of 276 = 2 + 7 + 6 = 15, which is divisible by 3.

Hence, 276 is divisible by 3.

(x) 179

Sum of all the digits of 179 = 1 + 7 + 9 = 17, which is not divisible by 3.

Hence, 179 is not divisible by 3.

2. Is 756 divisible by 3?

7 + 5 + 6 = 18 (18 is a multiple of 3)

Hence 756 is divisible by 3

We can verify that 756 is divisible by 3 by actual division.

3. In the number 46 * 8782, replace * by (i) a smallest digit and (ii) a largest digit to make it divisible by 3.

Solution:

The sum of the digits in the number 46 * 8782 = 4 + 6+ 8 + 7 + 8 + 2 = 35

(i) The number next to 35 which is divisible by 3 = 36.

Therefore, * is to be replaced by 1 i.e., 36 - 35 = 1;

Hence, the smallest digit 1 replaces * so as to make the number 4618782 divisible by 3.

(ii) We know that 35 + 7 = 42, which is divisible by 3.

Hence, the required largest digit 7 replaces * so as to make the number 4678782 divisible by 3.

Worksheet on Divisible by 3:

1. Fill the correct lowest possible digit in the blank space to make the number divisible by 3.

(i) 16335_

(ii) 20_984

(iii) 8422_1

(iv) 749_261

(v) 999_32

(vi) 1_7073

1. (i) 3

(ii) 4

(iii) 1

(iv) 1

(v) 1

(vi) 3

2. Which of the following numbers are divisible by 3?

(i) 875

(ii) 729

(iii) 3647

(iv) 8504

(v) 111

(vi) 3732

(vii) 6425

(viii) 963

2. (ii) 729

(v) 111

(vi) 3732

(viii) 963

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Properties of Divisibility.

Divisible by 2.

Divisible by 3.

Divisible by 4.

Divisible by 5.

Divisible by 6.

Divisible by 7.

Divisible by 8.

Divisible by 9.

Divisible by 10.

Divisible by 11.

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