Strategy : Prime Factorization

I am a subscriber of GMAT Hacks Question Of The Day where every alternate day of the weekday they email one Quant and one Verbal problem. Its a great way to make sure you are solving problems regularly and as many as possible. Whats also helpful is that they also mention the Answer(opens in a new window) and more importantly the explanation as to why the answer is what it is! You can and I suggest you should subscribe to this!

Today I came across a Quant problem in the subject of Prime Factorization. Though I didnt knew the answer, the explanation provided made sure I will never go wrong with such problems in future. For me it was like letting out a secret!

Since I am benefiting from a lot of blogs, its only fair that I share whatever I can on my blog!

Here it is -

The fastest way to find the number of factors of a large number is to take the exponent of each of the prime factors, raise it by one, and multiply them all together.


Lets take this into context with a problem from GMAT Hacks - 
***********************************************
How many different positive integers are factors of 378 ?
(A) 10
(B) 12
(C) 16
(D) 18
(E) 24

Answer is C.


Explanation - 


Start by finding the prime factorization of 378:
378 = 2(189)
= 2(9)(21)
= 2(3)(3)(3)(7)
= (2^1)(3^3)(7^1) 

In this case, the exponents are 1, 3, and 1. Raise them each by one, and you have 2, 4, and 2. Multiply them all together, and the result is 2(4)(2) = 16, choice (C)
***********************************************


There you go! Isn't it cool and REALLY helpful!