High School Problems in finding divisors using permutation,combination

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Finding the total number of divisors of a number involves using its prime factorization. For the number 120, which factors into 2^3, 3^1, and 5^1, the formula for calculating divisors is to add one to each of the exponents and then multiply the results. This means for 2, there are four options (2^0 to 2^3), for 3, two options (3^0 to 3^1), and for 5, two options (5^0 to 5^1). Therefore, the total number of divisors is calculated as (3+1)(1+1)(1+1) = 16. Understanding this mechanism clarifies how to determine the total number of divisors for any given number.
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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