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
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