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X is prime and y is positive integer, How many different factors of (2^3)*(x^y) are there?

1) x=5 2) y=3

How many different factors of (2^3)*(x^y) are there?
Always just two DIFFERENT: 2 and x
But x could be 2.
So
1) Is suff , just 2 factors
2) Is insuff, because x could be 2 or not, so it could be 1 or 2 different factors.

For any number that is written as the product of primes a^p*b^r*c^q,
where a,b,c are primes, and p,r,q are their powers, the number of factors
=(p+1)(r+1)(q+1). _________________

Well this is how we calculate..
If a number is raised to power of a prime number then the factor is n+1
e.g
2^3 means factors (3+1=4)
Lets see 2^3=8 (1,2,4,8)

Enother eg 2^3 * 5^4
Factors(3+1)*(4+1)=4*5=20
the catch here is tht the numbers should be prime...In our case both 2 and 5 are prime.

One more thing that I would like to add is that the number of distinct product pairs can be given by 1/2 times the number of distinct factors ( except for numbers which are prefect squares).

andy_gr8 wrote:

Well this is how we calculate.. If a number is raised to power of a prime number then the factor is n+1 e.g 2^3 means factors (3+1=4) Lets see 2^3=8 (1,2,4,8)

Enother eg 2^3 * 5^4 Factors(3+1)*(4+1)=4*5=20 the catch here is tht the numbers should be prime...In our case both 2 and 5 are prime.