Difference between factors and prime factors

Question

I don't know the difference between these two terms. For which things I should use which concept?

Could someone please help and explain this to me?

Thanks in advance!

chetan2u · Answer

Hi,
let me tell you with an example..
20.. this can be written in its basic form as 20= 2^2*5..
so prime factors are 3 in number--2,2, and 5....
different prime factors are 2 in number-- 2 and 5..
and number of factors are (2+1)(1+1) = 3*2= 6 in number--- 1,2,4,5,10,20...
so PRIME factors rae part of factors..

OptimusPrepJanielle · Answer

Consider the following example:

120 = (2^3)*3*5
This is the representation of any number in terms of prime factors.
You can get to this representation by dividing a number by prime numbers.

In this case, the prime factors would be 2, 2, 2, 3 and 5
Whereas the factors would be all the numbers (prime or not) that divide the number 120
Factors = 2, 4, 6, 8, 10, 15 ... etc.

In any particular question, you would be asked what ever you have to calculate factors or prime factors.

ccooley · Answer

I'll add that in general, if a problem just wants you to figure out how many prime factors (or 'unique prime factors', or just plain factors) there are, they have to be specific about which one they mean. Remember that 1 is a factor of every number, but because  1 isn't prime , it's never a prime factor!

But if you're solving a Number Properties problem that doesn't ask you specifically for the number of factors, but instead asks you a more general question about divisibility, you probably want the  prime factorization  specifically. In fact, I'd go so far as to say that every time you see a NP problem with a large integer in it, you should break it down to its prime factors right away. It's pretty rare to have to calculate the whole list of factors in the course of solving a more general problem, but pretty common to have to do a prime factorization.

deabas · Answer

Factors could be any numbers whose product is equal to the product (the result of multiplication)
for example, factors of 12 are: 1*12 = 2*6 = 3*4

On the other hand, the prime factors are also factors of a given number but they must prime (2, 3, 5, 7, 11, 13, 17, ...)
For example, the prime factors of 12 = (3*4) = 3*2*2 = 2^2+3

Good luck

Difference between factors and prime factors

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