Question

Which of the following numbers is completely divisible by 3.4 as well as 9
1) 710064
2) 13914
3) 70065
4) other

Answer 1

Given: Divisor are 3,4 and 9.

To find: Which of the numbers given in the options are completely divisible by 3.4 and 9 respectively.

Solution:

Check for option (1).

Check divisibility by 3.

Know that for a number to be completely divisible by 3 and 9, the sum of all its digit should be divisible by 3 and 9.

Therefore,

$710064=7+1+0+0+6+4$

          $=18$

Understand that 18 is completely divisible by 3 and 9.

Check divisibility by 4.

Know that for a number to be divisible by 4 the last digits of the number should be divisible by 4.

Last two digit of 710064 is 64.

$\[\frac{{64}}{{4}} = 16\]$

Therefore, the number 710064 is completely divisible by 4.

Hence, this is the correct option.

Check for option (2).

Check divisibility by 3.

Know that for a number to be completely divisible by 3 and 9, the sum of all its digit should be divisible by 3 and 9.

Therefore,

$13914=1+3+9+1+4$

          $=18$

Understand that 18 is completely divisible by 3 and 9.

Check divisibility by 4.

Know that for a number to be divisible by 4 the last digits of the number should be divisible by 4.

Last two digit of 13914 is 14.

$\[\frac{{14}}{{4}} = 3\frac{2}{4} \]$

Therefore, the number 710064 is not completely divisible by 4.

Hence, this is not the correct option.

Check for option (3).

Check divisibility by 3.

Know that for a number to be completely divisible by 3 and 9, the sum of all its digit should be divisible by 3 and 9.

Therefore,

$70065=7+0+0+6+5$

          $=18$

Understand that 18 is completely divisible by 3 and 9.

Check divisibility by 4.

Know that for a number to be divisible by 4 the last digits of the number should be divisible by 4.

Last two digit of 70065 is 65.

$\[\frac{{65}}{{4}} = 16\frac{1}{4} \]$

Therefore, the number 710064 is not completely divisible by 4.

Hence, this is not the correct option.