How many distinct positive factors does 32 have?
To find the number of factors of a positive integer, I need to factor it into prime factors first. I know that 32 is a power of 2, so I can write it as 2^5. Now, to count the factors, I can use a rule that says that if a number is of the form p^a * q^b * r^c * ..., where p, q, r, ... are distinct primes and a, b, c, ... are positive integers, then the number of factors is (a+1) * (b+1) * (c+1) * ... This is because for each prime factor, I can choose to include it in a factor from 0 to a times, for example, and multiply the choices together. So, for 32, which is of the form 2^5, the number of factors is (5+1) = 6. These factors are 1, 2, 4, 8, 16, and 32. 