Question

Using divisibility tests, determine if given number is divisible by $6$ :

$1258$

Answer 1

Rule for Divisibility by $6$ : A whole number is said to be divisible by 6 if it fulfils the two conditions given below.

• The given whole number should be divisible by $2$. A number is divisible by$2$ if the digit on the units place of the number is even, i.e., it is $0,2,4,6,and8$.
• The given whole number should be divisible by $3$. A number is divisible by $3$ if the sum of all digits of the number is exactly divisible by $3$.

Given number is $1258$.

As the given number ends with $8$. Hence, the given number $1258$ is divisible by $2$.

On adding all the digits of the given number, we obtain the sum as $16$ which is not divisible by $3$. Hence, the given number $1258$ is not divisible by $3$

∴ The number $1258$ is divisible by $2$ but not by $3$.

Hence, the given number $1258$ is not divisible by $6$.