Tell the factors

If p p is a prime number , how many factors does p 12 p^{12} have?

15 13 15 * p / 2 12 * p / 2 2 12

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3 solutions

Arulx Z
Mar 3, 2016

p n p^n has n + 1 n+1 factors, namely 1 1 , p p , p 2 p^2 , p 3 p^3 , ..., p n 1 p^{n-1} , p n p^n .

Due to the fundamental theorem of arithmetic, these are the only factors.

Harsh Chaudhary
Mar 1, 2016

p^n has n+1 factors.
p is a prime number and n is any positive integer.
e.g.
3^2=9 has 3 factors 1,3,9.
7^3=343 has 4 factors 1,7,49,343.
Power of any prime number can be prime factorized into n numbers.(n is the power of the prime number)
And 1 is factor of every number. Hence there are n+1 factors of p^n.


Sanyam Goel
Mar 26, 2016

@Harsh chaudhary problem is overrated !!!!!!!!

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