Question

What is the remainder when 12345678^75 is divided by 9?

Answer 1

Answer:

0

Step-by-step explanation:

Is quite easy as sum of all digits is multiple of 9 so there will no remainder

Answer 2

Given:

An exponent 12345678^75.

To find:

The remainder when the given exponential form is divided by 9.

Solution:

To answer this, first of all, we should know that a number is said to be divisible by 9 if the sum of all digits of that number is multiple of 9 or divisible by 9.

So, we have,

${(12345678)}^{75}$

Now,

After adding the digits of the number, we have,

$1 + 2 + 3 + 4 + 5 + 6 + 7 + 8$

$= 36$

As we know that 36 is divisible by 9, so there is no remainder when 12345678 is divisible by 9.

So,

$\frac{ {(12345678)}^{75} }{9}$

$= 0$

Hence, when the given exponential form is divided by 9, the remainder will be 0.