Factors

[Buix0065]

Hello,

I am trying to understand the concept of factors and prime factors.

For the problem "if P is the product of integers 1 - 30 inclusive, what is the greatest integer k for which 3^k is a factor of P?"



The solve is to determine the # of factors of 3 from all of the multiples of 3 1 - 30 inclusive. Can you help me understand what the connection is here, between the number of factors of 3 and 3^k being a factor of P?

Also, factoring it all out I get 3^14, 2^8, 5^2 and 7, not pertaining to the answer of the above question, but what can I draw from 7 not pairing up?

Thank you!

[blaster]

you need just count the 3`s

3+3*2+3*3+...+3*10

if you count all the 3`s you get 14

i think you missed one part of the question that's why don't understand the stem.

For the problem "if P is the product of integers 1 - 30 inclusive, what is the greatest integer k for which 3^k is a factor of P?"