Do 36 and 48 have the same amount of factors?

Answer 1

A fun way to figure out the number of factors, other than listing them all, is to use something called the TAU function. Take a number, such as 36 and write it in its prime factorization So 36=32 x 22 and 48=24 x 3 Now Tau(36) (which we say as Tau of 36) is the number of positive divisors of 36. Tau (48) is the number of positive divisors of 48. We compute Tau by looking at the exponents, 2 and 2 in the prime factorization and addiing 1 to each then multiplying. Don't worry about the base, ONLY the exponents! So Tau(36)=(2+1)(2+1)=9 Tau(48)=(4+1)(1+1)=10 which is greater than 9 so 48 has more factors. If you look at the links section with this question, I provided a webpage that helps a little more!