Question
Using divisibility tests, determine if number $297144$ is divisible by $6.$
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Answer
We know that a number is divisible by 6 if it is divisible by $2$ and $3$ both.
$i.\ $Divisibility by $2.$
$\because$ Unit's digit $= 4$
$\therefore$ $297144$ is divisible by $2.$
$ii.\ $Divisibility by $3.$
Sum of the digits $= 2 + 9 + 7 + 1 + 4 + 4 = 27,$
which is divisible by $3.$
$\therefore$ $297144$ is divisible by $3.$
Since, $297144$ is divisible by $2$ and $3$ both, so it is divisible by $6.$
$i.\ $Divisibility by $2.$
$\because$ Unit's digit $= 4$
$\therefore$ $297144$ is divisible by $2.$
$ii.\ $Divisibility by $3.$
Sum of the digits $= 2 + 9 + 7 + 1 + 4 + 4 = 27,$
which is divisible by $3.$
$\therefore$ $297144$ is divisible by $3.$
Since, $297144$ is divisible by $2$ and $3$ both, so it is divisible by $6.$
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