Question

What is the divisibility rule of 6?

Answer 1

Hint: We need to find the divisibility rule of 6. A number is divisible by 6 if it gives a zero remainder when divided by 6. We will be solving the given question using the divisibility rules of the numbers 2 and 3.

Complete step-by-step answer:
We are asked to find out the divisibility rule of 6. We will be solving the given question using the divisibility rules of the numbers 2 and 3.
The divisibility rule determines if a given number is divisible by a fixed divisor. It is a quick way to determine if one number is divisible by other without too many calculations.
In general terms, we can say that a number is divisible by 2 if it gives a zero remainder when divided by 2.
We have the divisibility rule of 2 is given as follows,
A given number is divisible by 2 if it ends with the digits 0,2,4,6,8.
All the even numbers end with digits 0,2,4,6,8 and are divisible by the number 2.
Example: 24
The number 24 ends with the digit 4 so, it is divisible by 2.
In general terms, we can say that a number is divisible by 3 if it gives a zero remainder when divided by 3.
We have the divisibility rule of 3 given as follows,
A given number is divisible by 3 if the sum of the digits of a number is divisible by 3.
Example: 27
The sum of the digits of the number 27 is $2+7=9$
The sum of the digits is divisible by 3 and so, 27 is divisible by 3.
Now, we have the divisibility rule of 6 as follows.
A given number is divisible by 6 if it ends with digits 0,2,4,6,8 and the sum of the digits is divisible by 3.
In simple terms, we can say that a given number is divisible by 6 if it is divisible by both 2 and 3.
Example: 42
The number 42 ends with the digit 2 so it is divisible by 2.
The sum of the digits of the number 42 is $4+2=6$
The sum of the digits is divisible by 3 and so, 42 is divisible by 3.
Therefore, 42 is divisible by 6.

Note: The divisibility rule determines whether a number is divisible by another number without performing a long division. We must remember that a given number is divisible by 6 only if it gives a zero remainder when divided by 6.