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Topic: A matter of factorization 


After a little bit of pencil pushing, you find that your favorite number can be expressed in the prime factored form of (a^x) * (b^y)* (c^z) . . . etc. , where a, b, c . . . are distinct primes, and x, y, z . . . are integers. How many factors does your number have? How can you show that your answer must be correct? e.g. 16200 can be expressed as (2^3) (3 ^4) (5^2) . How many factors (prime and nonprime) does 16200 contain? Jack Shalom 


There're a couple ways of looking at that. The simplest is this: consider 2^x * 3^y * 5^z now, let x, y, and z range between 0 and the actual correct exponent for 16200 Each of those possibilities will correspond to a unique number that divides 16200. (if you don't want do count 1 as a factor, just subtract 1 from the answer..) so we have 4*5*3 = 60 possibilities. or 59 not counting 1. or 58 not counting either 1 or 16200. 