Problem #PRU-100220

Problems Algebra and arithmetic Number theory. Divisibility Divisibility of a number. General properties Divisibility rules

Problem

One day Friday multiplied all the numbers from 1 to 100. The product appeared to be a pretty large number, and he added all the digits of that number to receive a new smaller number. Even then he did not think the number was small enough, and added all the digits again to receive a new number. He continued this process of adding all the digits of the newly obtained number again and again, until finally he received a one-digit number. Can you tell what number was it?