Question

the number 111111111111 is divisible by
a) 9 and 11
b) 5 and 11
c) 3 and 09
d) 3 and 11

Answer 1

Answer:

Option d) is the correct answer to the given problem.

Step-by-step explanation:

Given: The number is 111111111111.

We have to find the above number is divisible by which number.

As we know, if the sum of all the digits of the given number is divisible by 3, then the number is divisible by 3.

We are solving in the following way:

We have,

The number is 111111111111.

The sum of all the digits of the given number is:

$1+1+1+1+1+1+1+1+1+1+1+1=12$

and$\frac{12}{3} =4$

Hence, the number 111111111111is divisible by 3.

We know that the difference of the sums of alternating digits is 0 or divisible by 11, then the number is divisible by 11.

The difference of the sums of alternating digits will be:

$1+1+1+1+1+1=6 \ and\ 1+1+1+1+1+1=6$

And $6-6=0$

The number 111,111,111,111, is divisible by 11 because the difference of the sums of alternating digits is 0.