Q. 74.2( 9 Votes )

# Check whether 456 and 618 are divisible by 6? Also check whether 6 divides the sum of 456 and 618?

Answer :

Given, “456” and “618” two numbers.

Need to find out it is divisible by 6 and also sum of the two numbers is divisible by 6.

⇒ prime factors of 6 are 2,3

⇒ 456 is divisible by 2 since, units place of a number’456’ is 6 which is divisible by 2.

⇒ Sum of the digits of 456 must be divisible by 3

⇒ 4 + 5 + 6 = 15 is divisible by 3.

∴ 456 is divisible by 6.

⇒ 618 is divisible by 2. Since, units place of a number ‘618’ is 8 which is divisible by 2.

⇒ Sum of the digits of 618 must be divisible by 3.

⇒ 6 + 1 + 8 = 15 is divisible by 3.

∴ 618 is divisible by 6.

Sum of 456, 618 = 456 + 618

= 1074 is divisible by 6 needs to be calculated

⇒ 1074 is divisible by 2 since, unit place of a number ‘1074’ is 4 which is divisible by 2.

⇒ Sum of the digits of 1074 must be divisible by 3.

⇒ 1 + 0 + 7 + 4 = 12 is divisible by 3.

∴ 1074 is divisible by 6

Hence, 456,618 and their sum is divisible by 6.

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