What number above 100 has the most factors?

Answer 1

There is no such number. No matter how high you go, there will always be another larger number with more factors.

Let's say you take the number 101. This is a Prime number, so its prime factorization is 101 = 1 * 101

Now let's look for a number with an additional prime factor. In order to do this, we multiple 101 by the smallest prime number: 2

101 * 2 = 202

This new number now has two prime factors: 2 and 101

If we keep multiplying our numbers by 2, we will keep getting one more prime factor each time. This will continue as our number approaches infinity.