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Re: Help: Factors problem !! [#permalink]
15 Aug 2010, 03:04

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praveengmat wrote:

How many factors does 36^2 have? A 2 B 8 C 24 D 25 E 26 Please help as to how to solve this problem with 1 minute !!

Finding the Number of Factors of an Integer:

First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2

Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors.

Back to the original question:

How many factors does 36^2 have?

36^2=(2^2*3^2)^2=2^4*3^4 --> # of factors (4+1)*(4+1)=25.

Answer: D.

Or another way: 36^2 is a perfect square, # of factors of perfect square is always odd (as perfect square has even powers of its primes and when adding 1 to each and multiplying them as in above formula you'll get the multiplication of odd numbers which is odd). Only odd answer in answer choices is 25.

Re: Help: Factors problem !! [#permalink]
15 Aug 2010, 03:11

Bunuel wrote:

praveengmat wrote:

How many factors does 36^2 have? A 2 B 8 C 24 D 25 E 26 Please help as to how to solve this problem with 1 minute !!

Finding the Number of Factors of an Integer:

First make prime factorization of an integer n=a^p*b^q*c^r, where a, b, and c are prime factors of n and p, q, and r are their powers.

The number of factors of n will be expressed by the formula (p+1)(q+1)(r+1). NOTE: this will include 1 and n itself.

Example: Finding the number of all factors of 450: 450=2^1*3^2*5^2

Total number of factors of 450 including 1 and 450 itself is (1+1)*(2+1)*(2+1)=2*3*3=18 factors.

Back to the original question:

How many factors does 36^2 have?

36^2=(2^2*3^2)^2=2^4*3^4 --> # of factors (4+1)*(4+1)=25.

Answer: D.

Or another way: 36^2 is a perfect square, # of factors of perfect square is always odd (as perfect square has even powers of its primes and when adding 1 to each and multiplying them as in above formula you'll get the multiplication of odd numbers which is odd). Only odd answer in answer choices is 25.

Re: Help: Factors problem !! [#permalink]
14 Oct 2010, 13:58

1

This post received KUDOS

Factors of a perfect square can be derived by using prime factorization and then using the formula to find perfect square's factors.

In this case (36)^2= (2^2*3^2)^2=2^4*3^4 or (36)^2=(6^2)^2=(6)^4=(2*3)^4=2^4*3^4

And now you can use the formula explained above by Bunuel to determine the answer, which is (4+1)*(4+1)=5*5=25=Odd(Trick is there must be odd number of factors of a perfect square and only 25 is odd in answer choices, so it can be solved within 30 seconds or less )

Please! go through the GMAT Math Book by GMAT CLUB (written by bunuel & walker), all of these tips & tricks are written there. (even I have compiled them in one .pdf file and is shared here on Math forum) _________________

"Don't be afraid of the space between your dreams and reality. If you can dream it, you can make it so." Target=780 http://challengemba.blogspot.com Kudos??

Re: Help: Factors problem !! [#permalink]
01 Sep 2011, 19:17

The Easy Answer! (Applicable only in case of perfect square numbers) A perfect square always have a odd number of factors. 36^2 is a perfect square. Given the answer choices, the only odd number of factor is 25.

Re: How many factors does 36^2 have? [#permalink]
25 Oct 2014, 05:23

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