Problem Solving

--------
How many factors does 36^2 have?
A) 2
B) 8
C) 24
D) 25
E) 26

The ans is : D
----------
But I found B becouse 2*2*2*2*3*3*3*3

Can any one pls explain me why D is correct.

Thanks
Sarwan

Did you count the factor 1 ?

sarwan wrote:--------
How many factors does 36^2 have?
A) 2
B) 8
C) 24
D) 25
E) 26

The ans is : D
----------
But I found B becouse 2*2*2*2*3*3*3*3

Can any one pls explain me why D is correct.

Thanks
Sarwan

36^2 = 2^4*3^4

so factors = (4+1)(4+1) [Power of each prime factor + 1]
=25

Rule -> If n = a^x * b^y * c^z where a,b,c are prime numbers then number of factors that n have (including 1 and n) is (x+1)*(y+1)*(z+1)

Always when solving the factors problem,we should include 1

Patrick_GMATFix wrote:Did you count the factor 1 ?

If we shall count the factor 1 then it can be upto infinite.
Can you pls explain me how we can consider 1 ?

Thanks
Sarwan

rahulmehra13 wrote:

sarwan wrote:--------
How many factors does 36^2 have?
A) 2
B) 8
C) 24
D) 25
E) 26

The ans is : D
----------
But I found B becouse 2*2*2*2*3*3*3*3

Can any one pls explain me why D is correct.

Thanks
Sarwan

36^2 = 2^4*3^4

so factors = (4+1)(4+1) [Power of each prime factor + 1]
=25

Rule -> If n = a^x * b^y * c^z where a,b,c are prime numbers then number of factors that n have (including 1 and n) is (x+1)*(y+1)*(z+1)

Thanks Rahul
I got it what you want to say but still I could not understood why we need to consider 1.

~Sarwan

sarwan wrote:

Patrick_GMATFix wrote:Did you count the factor 1 ?

If we shall count the factor 1 then it can be upto infinite.
Can you pls explain me how we can consider 1 ?

Thanks
Sarwan

X is a factor of Y if Y can be evenly divided by X (such that there is no remainder). 1 is a factor of every positive integer since every such integer can be evenly divided by 1 . So if you were asked "what are the factors of 6?", you should reply "1, 2, 3, and 6". There are 4 positive factors (counting 1 doesn't lead to any consideration of infinity).

Because it's easy to forget to include 1 and the number itself (6 in the example above), I like to start counting factors with those two, and then find the other factors that exist between the two.

-Patrick

rahulmehra13 wrote: 36^2 = 2^4*3^4

so factors = (4+1)(4+1) [Power of each prime factor + 1]
=25

Rule -> If n = a^x * b^y * c^z where a,b,c are prime numbers then number of factors that n have (including 1 and n) is (x+1)*(y+1)*(z+1)

Thanks Rahul, that's a fantastic tip

sarwan wrote:--------
How many factors does 36^2 have?
A) 2
B) 8
C) 24
D) 25
E) 26

The ans is : D
----------
But I found B becouse 2*2*2*2*3*3*3*3

Can any one pls explain me why D is correct.

Thanks
Sarwan

Hi,

you've answered the question:

How many prime factors does 36^2 have?

which is not the question asked.

An extremely common trap on the GMAT is what we at Kaplan often refer to as "the right answer to the wrong question". If there's a common way to misinterpret a math problem, there will almost always be an answer choice to punish people for making that mistake.

(A) is another example of that error; 2 is the answer to the question "How many distinct prime factors does 36^2 have?"

The formula provided by Rahul is the quickest way to solve this problem; for smaller numbers, we could also just brute force the answer (i.e. list out all the factors in pairs, starting with 1 and the number).

Patrick_GMATFix wrote:

sarwan wrote:

Patrick_GMATFix wrote:Did you count the factor 1 ?

If we shall count the factor 1 then it can be upto infinite.
Can you pls explain me how we can consider 1 ?

Thanks
Sarwan

X is a factor of Y if Y can be evenly divided by X (such that there is no remainder). 1 is a factor of every positive integer since every such integer can be evenly divided by 1 . So if you were asked "what are the factors of 6?", you should reply "1, 2, 3, and 6". There are 4 positive factors (counting 1 doesn't lead to any consideration of infinity).

Because it's easy to forget to include 1 and the number itself (6 in the example above), I like to start counting factors with those two, and then find the other factors that exist between the two.

-Patrick

Hi Patrick and Rahul,

Thanks both of you...Now it is clear. These explations are really helped me to understand the concept.

~Sarwan