From 1 to 100 select 26 distinct numbers: pigeonhole principle

Question

From 1 to 100 select 26 distinct numbers, there must exist one number which divides the product of the other 25 numbers.

This seems to be an easy application of the pigeonhole principle, but I could not figure out the exact argument. Can someone help?

Answer 1

Hint to get you started:

• How many primes numbers are there less than $100$?