if p,r, and s are three different prime numbers > 2, n=pXrXs

[anp]

im not sure how to solve this, i tried plugging in random prime numbers but the answers i got werent the answer that is given.

if p,r, and s are three different prime numbers greater than 2, and n=p X r X s, how many positive factors including 1 does n have?

 

[pka]

Re: prime numbers

if p,r, and s are three different prime numbers greater than 2, and n=p X r X s, how many positive factors including 1 does n have?

The answer is eight.
Any factor of \(\displaystyle p\cdot r\cdot s\) looks like \(\displaystyle p^k\cdot r^m\cdot s^n\) where \(\displaystyle 0\le k\le 1,~0\le m\le 1,~0\le n\le 1\).

Example: \(\displaystyle 3\cdot 5\cdot 7 =105\) factors 1, 3, 5, 7, 15, 21, 35, 105.

BTW: There is no need to require that the prime could be 2 just they are all difference.

 

[Mrspi]

im not sure how to solve this, i tried plugging in random prime numbers but the answers i got werent the answer that is given.

if p,r, and s are three different prime numbers greater than 2, and n=p X r X s, how many positive factors including 1 does n have?

If p, r and s are DIFFERENT primes, then there is no factor common to p, r, and s other than 1.

So...the factors of p*r*s would be

1
p
r
s
p*r
p*s
r*s
p*r*s

As pka stated, that gives you 8 different factors.