60, 72, 84, 90 and 96. They all have 12 factors
Using prime factorization, there are 2 three digit numbers with 9 factors: 512 and 768. There are no three digit numbers with 10 or more prime factors. 512=2^9 and 768=3*2^8
The squares of most 2 digit prime numbers. For example 2809, which is the square of 53, has 3 factors : 1, 53 and 2809 itself.
One way to solve this is to multiply the lowest prime numbers together, starting from 2: 2x3=6. 6x5=30. Multiplying by 7 would yield a 3-digit number, so we are looking for all 2-digit numbers with 3 distinct prime factors. We already have 30. 2x3x7=42. 2x3x11=66. 2x3x13=78. 2x5x7=70. So, to answer the original question, the 2-digit numbers that have the most factors in their prime factorization are, in ascending order, 30, 42, 66, 70, and 78.
If you're asking about distinct prime factors, there are eight numbers tied with three of them. If not, 64 has six twos.
Well, honey, single digit factors of a number are just the numbers that can divide into that number without leaving a remainder. So, for example, the single digit factors of 12 are 1, 2, 3, 4, and 6. It's like finding out who's invited to the party before you start breaking out the cake.