Question

Using the divisibility test, determine $1586$ is divisible by $2$, by $3$, by $4$, by $5$, by $6$, by $8$, by $9$, by $10$, by $11$(Say yes or no)

Number	Divisible by
	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$
$1586$

Answer 1

Step $1:$ Finding whether $1586$ is divisible by $2$, by $5$ by $10$ or not:

Divisibility test of $2$: A number is divisible by $2$, when the number is ending with $0,2,4,6,8$

Divisibility test of $5$: A number is divisible by $5$, when the number is ending with either $0$ or $5$

Divisibility test of $10$: A number is divisible by $10$, when the number is ending with $0$

Since, $1586$ is ending with $6$, therefore $1586$ is divisible by $2$ and not divisible by $5$ and not by $10$.

Step $2:$ Finding whether $1586$ is divisible by $3$, by $9$ or not:

Divisibility test of $3$: A number is divisible by $3$, when the sum of the digits of the number is divisible by $3$

Divisibility test of $9$: A number is divisible by $9$, when the sum of the digits of the number is divisible by $9$

The given number is $1586$

Sum of the digits of $1586\Rightarrow 1+5+8+6=20$

$20$ is not divisible by $3$, therefore $1586$ is not divisible by $3$

$20$ is not divisible by $9$, therefore $1586$ is not divisible by $9$

Step $3:$ Finding whether $1586$ is divisible by $4$, by $8$ or not:

Divisibility test of $4$: A number is divisible by $4$, when the last two digits of the number is divisible by $4$

Divisibility test of $8$: A number is divisible by $8$, when the last three digits of the number is divisible by $8$

The given number is $1586$

Last two digits in $1586$ is $86$

Clearly, $86$$÷4=$$21.5$

Clearly, $86$ is not divisible by $4$, therefore $1586$ is not divisible by $4$

Last three digits in $1586$ is $586$

Clearly, $586$$÷8=$$73.25$

Clearly, $586$ is not divisible by $8$,therefore $1586$ is not divisible by $8$

Step $4:$ Finding whether $1586$ is divisible by $6$, by $11$ or not:

Divisibility test of $6$: A number is divisible by $6$, when the number is divisible by both $2$ and $3$

As, $1586$ is divisible by $2$ but not by $3$.

Hence, $1586$ is not divisible by $6$

Divisibility test for $11$: A number is divisible by $11$, if the difference between the sum of the digits at even places and the sum of the digits at odd places(starting from the ones place) is divisible by $11$.

The given number is $1586$

Sum of the digit at odd places $=6+5=11$

Sum of the digit at even places $=8+1=9$

The difference $=11-9=2$ which is not divisible by $11$.

Therefore, the number $1586$ is not divisible by $11$.

Therefore, the answer is

Number	Divisible by
	$2$	$3$	$4$	$5$	$6$	$8$	$9$	$10$	$11$
$1586$	Yes	No	No	No	No	No	No	No	No