Question

Suppose you write the value of 100! as a number. Then suppose you add up the digits of the number, and get a new number. Then add the digits of the new number and repeat the process until you get a single digit. What is that digit?

Answer 1

The single digit obtained by repeatedly adding up the digits of 100! is 3.

Step-by-step explanation:

To find the single digit obtained by repeatedly adding up the digits of 100!, we need to calculate the factorial of 100 and then perform the required operations. The factorial of 100 is the product of all positive integers from 1 to 100. We can use the concept of integer powers of 10 to find the result.

First, let's calculate the factorial of 100:

100! = 100 × 99 × 98 × ... × 3 × 2 × 1

Now, let's write the value of 100! as a number:

100! = 9332621544394415268169923885626670049071596826438...

After adding up the digits of this number, we get a new number:

9 + 3 + 3 + 2 + ... + 8 + 6 + 4 + 3 + 8 + ...

Repeating this process of adding up the digits until we get a single digit:

9 + 3 + 3 + 2 + ... + 8 + 6 + 4 + 3 + 8 + ... = 4 + 7 + 2 + 5 + 4 + 6 + ... = 28 + 22 + 10 + ... = 1 + 0 + 2 + ... = 3

Therefore, the single digit obtained by repeatedly adding up the digits of 100! is 3.