Question

Determine whether $75689604$ is divisible by $2,4$or $8$

Answer 1

Step 1 - Checking the divisibility by $2$

A number is divisible by $2$ if its last ( unit’s) digit is divisible by $2$ I.e., if its last digit is $0,2,4,6,8$

The given number has $4$ in its unit's place , which is divisible by $2$ $\left[\because 2\times 2=4\right]$

Therefore $75689604$ is divisible by $2$

Step 2 - Checking the divisibility by $4$

A number is divisible by $4$ if the number formed by its last two ( unit’s and ten’s ) digits is divisible by $4$.

The number formed by last two digits of $75689604$ is $04$ i.e., $4$ which is divisible by $4$ $\left[\because 4\times 1=4\right]$

Therefore $75689604$ is divisible by $4$

Step 3 - Checking the divisibility by $8$

A number is divisible by $8$ if the number formed by its last three ( unit’s , ten’s and hundred’s ) digits is divisible by $8$.

The number formed by last three digits of $75689604$ is $604$ which is not divisible by $8$.

Therefore $75689604$ is not divisible by $8$

Hence , $75689604$ is divisible by $2,4$ but not divisible by $8$