Coaching Centre
Divisibility tests
Quick tests to check whether a number is divisible by 2, 3, 4, 5, 6, 8, 9 and 10 without dividing.
The tests
Is $5742$ divisible by $3$, $6$ and $9$?
Digit sum: $5 + 7 + 4 + 2 = 18$. That is divisible by $3$ and by $9$.
It is even, so it is divisible by $2$, and therefore by $6$. Yes to all three.
Test for 9
Digit sum divisible by 9.
Test for 4
Last two digits divisible by 4.
Test for 6
Divisible by both 2 and 3.
Is $5742$ divisible by $9$?
Digit sum $18$.
Is $1234$ divisible by $4$?
$34$ is not divisible by $4$.
Is $7128$ divisible by $8$?
$128 = 8 \times 16$.
Which number is divisible by $6$?
$432$ is even and its digit sum is $9$.
Is $2\,001$ divisible by $3$?
Digit sum $3$.
Which single digit replaces $\square$ so that $5\square 2$ is divisible by $9$?
The digit sum must be $9$: $5 + 2 + 2 = 9$.
A number is divisible by $10$ when:
Last digit $0$.
Is $4\,725$ divisible by $5$ and $9$?
Ends in $5$; digit sum $18$.
New numbers every time. Keep going until you get five in a row.