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    Jphardes Posts: 1, Reputation: 1
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    #1

    Apr 19, 2012, 07:29 AM
    Positive integral factors of 3000000000
    How many positive integral factors does 3000000000 have?
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    Apr 19, 2012, 10:04 AM
    I will show you how to do this for another number, then you can apply the same technique to this problem.

    To find the number of integral positive factors for a number first break it into its prime factors, then calculate how many ways those prime factors can be combined. For example: for the number 720 the prime factors are 2x2x2x2x3x3x5. So there are 4 two's, 3 threes, and 1 five. Any integral factor will have between zero and this quantity of numbers of each prime factor - hence it could have either 0, 1, 2, 3, or 4 two's (5 possibilities) , plus 0, 1, or 2 threes (3 possibilities), and either 0 or 1 five (2 possibilities). Thus the number of combinations that are possible is 5 x 3 x 2 = 30, so there are 30 positive integral factors of 720. Note that this provides all combinations, including both 1 and 720.

    For your problem you need to start by factoring 3,000,000,000 into its primes. Post back with your answer and we'll check it for you.
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