What two digit number with the greatest number of factors?

Answer 1

There could be two answers for this depending on what you are actually looking for. If you are looking for the number that takes the most prime factors to create, then I'd guess it's tied between 64 and 96.

64's prime factors are 2*2*2*2*2*2

96's prime factors are 2*2*2*2*2*3

Since you can't really get much smaller than those prime factors there shouldn't be anything with more of them.

If your goal was simply what number can be divided by the most other numbers then there are 5 that tie. 60, 72, 84, 90, and 96 each have 12 numbers that can factor into them.

60 72 84 90 96 1*60 1*72 1*84 1*90 1*96

2*30 2*36 2*42 2*45 2*48

3*20 3*24 3*28 3*30 3*32

4*15 4*18 4*21 5*18 4*24

5*12 6*12 6*14 6*15 6*16

6*10 8*9 7*12 9*10 8*12