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B Problems in finding divisors using permutation,combination

  1. Jul 19, 2016 #1
    I am facing some problems when I am told to find the total number of divisors of a certain number using permutations and combinations.Here is an example:
    What is the total number of divisors of the number 120?
    Ans:
    120=2^3*3^1*5^1
    The total number of divisors:(3+1)(1+1)(1+1)=16

    I just don't get it why do we add 1 with the powers of the divisors and then multiply them?And by doing this how can we find the total number of divisors?I have just become fully confused and unable to understand the mechanism.Can anyone please help me to understand this?
    With regards,
    Shafia.
     
  2. jcsd
  3. Jul 19, 2016 #2
    Actually its like this
    In any divisor of the number 120, 2 can occur in four ways namely: 2^0, 2^1, 2^2, 2^3
    Similarly 3 can occur as : 3^0, 3^1
    5 can occur as : 5^0, 5^1
    Hence (3+1)*(1+1)*(1+1)= 16
     
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