Question

Classify the following numbers as divisible by 3, 4 & 9. 111, 72, 108, 369, 999, 960 ​

Answer 1

Answer:

111 divisible by 3

72 divisible by 3 as well as by 2

108 divisible by 3 as well as 2 as well as 4

999 divisible by 3 as well as 9

960 divisible by 3 as well as 4

Answer 2

Given:

Numbers $111,72,108,369,999,960$

To find:

To check if the numbers are divisible by $3,4,9$.

Solution:

If we add the digits of a number and if the sum results in multiples of $3$, then that number is divisible by $3.$

If we add the digits of a number and if the sum results in multiples of $9$, then that number is divisible by

If the last two digits of a number are divisible by $4$, then the entire number is divisible by

Considering the number $111$. Add the digits to see if it is a multiple of $3$.

$1+1+1=3$.

The sum obtained is $3$ which is a multiple of

$111$ is divisible by $3$ only.

Consider the number $72$.

$7+2=9$

$9$ is a multiple of both $3$ and

$72$ on dividing by $4$ results in a quotient of $18$.

Hence, $72$ is divisible by $3,4,9$.

Consider the number $108$.

$1+0+8=9$

$9$ is a multiple of both $3$ and

The last two digits $08$ is divisible by $4$. Hence, $108$ is divisible by

Thus, $108$ is divisible by $3,4,9$.

Consider the number $369$.

$3+6+9=18$

$18$ is a multiple of both $3$ and $9$. Hence, $369$ is divisible by both

The last two digits $69$ is not divisible by $4$. Hence, $369$ is not divisible by

Thus, $369$ is divisible by $3$ and $9$ and not by $4$.

Consider the number $999$.

$9+9+9=27$

$27$ is a multiple of both $3$ and $9$. Hence, $999$ is divisible by both

The last two digits $99$ is not divisible by $4$. Hence, $999$ is not divisible by

Thus, $999$ is divisible by $3$ and $9$ and not by $4$.

Consider the number $960$.

$9+6+0=15$

$15$ is a multiple of $3$ and not of $9$. Hence, $960$ is divisible by

The last two digits $60$ is divisible by $4$ having a quotient of $15$. Hence, $960$ is divisible by

Thus, $960$ is divisible by $3$ and $4$ and not by $9$.

111 is divisible by 3 only.

72 is divisible by 3, 4, and 9.

108 is divisible by 3, 4, and 9.

369 is divisible by 3 and 9 only.

999 is divisible by 3 and 9 only.

960 is divisible by 3 and 4 only.