# Divisible by 6

This topic on divisible by 6 will discuss about the divisibility rule of 6 and few example on the same.

Divisibility Rule of 6:

A number is divisible by 6 if the prime factor of that is 2 & 3 is divisible by 6.

For Example: 216

216 is divisible by 2 as the last digit 6 is divisible by 2

The sum of the digits = 2 + 1 + 6 = 9

Now, 9 is divisible by 3 hence, 216 is also divisible by 3

Therefore, 216 is divisible by 6 as the number is divisible by 2 and 3.

Here are few examples on the divisibility rule of 6:

1. Check whether the following numbers are divisible by 6 and state the reason.

(i) 744

(ii) 564

(iii) 457

(iv) 455

(v) 336

(vi) 360

(vii) 886

(viii) 763

(ix) 426

(x) 1551

Solution:

(i) 744

The last digit is 4 hence the number is divisible by 2

Sum of the digits = 7 + 4 + 4 = 15

15 is divisible by 3 hence, 744 is divisible by 3

744 is divisible by both 2 and 3 hence, the number is also divisible by 6

(ii) 564

The last digit is 4 hence the number is divisible by 2

In 564, Sum of the digits = 5 + 6 + 4 = 15

15 is divisible by 3 hence, 564 is divisible by 3

564 is divisible by both 2 and 3 hence, the number is also divisible by 6

(iii) 457

7 is the last digit hence the number 457 Is not divisible by 2

Sum of the digits = 4 + 5 + 7 = 16

16 is not divisible by 3 hence, 457 is also not divisible by 3

Hence, 457 is also not divisible by 6

(iv) 455

The last digit is 5 hence the number is divisible by 2

In 455, Sum of the digits = 4 + 5 + 5 = 14

14 is not divisible by 3 hence, 455 is not divisible by 3

Therefore, 455 is not divisible by 6

(v) 336

In 336 6 is the last digit and hence it is divisible by 2

Sum of the digits = 3 + 3 + 6 = 15

15 is divisible by 3 hence, 336 is divisible by 3

336 is divisible by both 2 and 3 hence, the number is also divisible by 6

(vi) 360

0 is the last digit hence, 360 is divisible by 2

Sum of the digits = 3 + 6 + 0 = 9

15 is divisible by 3 hence, 360 is divisible by 3

360 is divisible by both 2 and 3 hence, the number 360 is also divisible by 6

2. Rewrite the series with the numbers that are divisible by 6 with a different color.

36    66    995    62    78    216    480    996    6000    8682    65400    985    63547

Solution:

36    66    995    62    78    216    480    996    6000    8682    65400    985    635471