Problems in finding divisors using permutation,combination

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SUMMARY

The discussion focuses on calculating the total number of divisors of the number 120 using the formula derived from its prime factorization. The prime factorization of 120 is expressed as 23 * 31 * 51. To find the total number of divisors, one must add 1 to each of the exponents in the prime factorization and then multiply the results: (3+1)(1+1)(1+1) = 16. This method is essential for understanding divisor counting in number theory.

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Shafia Zahin
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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.
 
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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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