K = wxyz, where w, x, y, z are prime numbers. Not including 1 and K, how many factors does K have?
I assume it's K=w*x*y*z
, where w, x, y, z are prime numbers.Finding the Number of Factors of an Integer
First make prime factorization of an integer n=a^p*b^q*c^r
, where a
, and c
are prime factors of n
, and r
are their powers.
The number of factors of n
will be expressed by the formula (p+1)(q+1)(r+1)
this will include 1 and n itself.Example:
Finding the number of all factors of 450: 450=2^1*3^2*5^2
Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18
So if K=w^1*x^1*y^1*z^1
, where w, x, y, z are prime numbers then number of factors of K including 1 and K itself would be (1+1)(1+1)(1+1)(1+1)=16
and excluding 1 and K: 16-2=14
For more on this check Number Theory chapter of Math Book: math-number-theory-88376.html
Hope it helps.
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