What is the remainder

when 5×55×555×…×555,555,555 is divided by 100?

25

you are absolutely wrong hans,...the answer is just 1 ....the exact result is [179474346464282065871418229594200357890625/4]....so the remainder is 1...

To find the remainder when a large number is divided by 100, we can use the concept of modular arithmetic.

Since we are given that the number is a product of many 5s, let's simplify it by breaking it down into smaller parts.

First, let's consider the remainder when 5 is divided by 100.
Since 5 divided by 100 leaves a remainder of 5 itself, we can say that 5 ≡ 5 (mod 100).

Next, let's consider the remainder when 55 is divided by 100.
Dividing 55 by 100 gives a quotient of 0 and a remainder of 55. Therefore, 55 ≡ 55 (mod 100).

Now, let's consider the remainder when 555 is divided by 100.
Dividing 555 by 100 gives a quotient of 5 and a remainder of 55. Therefore, 555 ≡ 55 (mod 100).

We can see a pattern emerging here. Ultimately, the remainder when a number composed of n digits of 5 (e.g., 555, 5555, etc.) is divided by 100 will always be 55.

So, when we multiply all these numbers together, the remainder will still be 55.

Hence, the remainder when 5 × 55 × 555 × ... × 555,555,555 is divided by 100 is 55.