Question

Check the divisibility conditions of $2,3$ for the following numbers:

$\left(i\right)872645$

$\left(ii\right)46523$

$\left(iii\right)71232$

$\left(iv\right)89632$

$\left(v\right)251730$

Answer 1

A natural number is divisible by $2$ if and only if, the digit in its units's place is either $2$ or $4$ or $6$ or $8$ or $0$

A natural number is divisible by $3$ if and only if, the sum of the digits is divisible by $3$

Numbers	Divisibility by $2$	Divisibility by $3$
$\left(i\right)872645$	The last digit is $5$.So it is not divisible by $2$	$8+7+2+6+4+5=32$ is not divisible by $3$. Hence $872645$ is not divisible by $3$
$\left(ii\right)46523$	The last digit is $3$.So it is not divisible by $2$	$4+6+5+2+3=20$ is not divisible by $3$.Hence $46523$ is not divisible by $3$
$\left(iii\right)71232$	The last digit is $2$.So it is divisible by $2$	$7+1+2+3+2=15$ is divisible by $3$. Hence 71232 is divisible by 3.
$\left(iv\right)89632$	The last digit is $2$.So it is divisible by $2$	$8+9+6+3+2=28$ is not divisible by $3$. Hence 89632 is not divisible by 3.
$\left(v\right)251730$	The last digit is $0$.So it is divisible by $2$	$2+5+1+7+3+0=18$ is divisible by $3$. Hence $251730$ is divisible by $3$