Power Factors

[alecm666]

How many factors does 36^2 have? (CAT questions)
the answer is 25.


I want to know why we use primes to solve the problem? Because my math is really basic and dont know anything about primes' application expect its definition.

If let say the question is : how many factors does 22^2 have?
Should the answer be:
(11 * 2)^2
= 11, 11, 2 , 2
I can have zero to three 11; same for 2. So the answer is 3*3 = 9?

[RonPurewal]

If let say the question is : how many factors does 22^2 have?
Should the answer be:
(11 * 2)^2
= 11, 11, 2 , 2
I can have zero to three 11; same for 2. So the answer is 3*3 = 9?

yes, exactly.

if this is still uncomfortably abstract for you, you can actually list out the factors thus formed:
none of either = 1
2 = 2
2•2 = 4
11 = 11
2•11 = 22
2•2•11 = 44
11•11 = 121
2•11•11 = 242
2•2•11•11 = 484 {= the original number 22^2)

of course, it's not necessary to do this-- in fact, you don't even need to know that the original number is 484!-- but it may be edifying.