If N = 144, then what is the number of ways of expressing N as a produ

Question

If N = 144, then what is the number of ways of expressing N as a product of 2 positive factors when the factors are not necessarily distinct?

A. 7
B. 8 
C. 10
D. 15
E. 16

Are You Up For the Challenge: 700 Level Questions

IanStewart · Answer

The number 144 = (2^4)(3^2) has 5*3 = 15 divisors in total. So we can write 144 as a product of two positive factors in 15 different ways, if the order of the two factors matters (those ways will be 1*144, 2*72, 3*48, and so on). Here we're counting, for example, 2*72 and 72*2 as two different ways to write 144 as a product.

If instead the order of the two factors is not supposed to matter, then we have 14 products in our list above that actually occur twice, once in each order, and if we're only meant to count those once, we should only count them 7 times. We have one product, 12*12, where order was already irrelevant, so if the order of the factors is not meant to be important, the answer is 8.

There's no way to really guess which answer is right, because there's no way to know what the question means what it talks about a "way to express N as a product of two positive factors".

sanjitscorps18 · Answer

The question should specifically mention that the order does not matter, hence we don't count the factor pairs as duplicate. If the order does not matter then the answer should be 8.

Option B

The answer has already been shared hence no creating a separate post for that

versewriter · Answer

Here is the solution

We know the total factor of 144 are 15. That means we can write the 144 in a 15 ways. We assume that the repeated factors are not to be considered as the question is asking about the not distinct factors.

1*144
2*72
3*48
4*36
8*18
9*16
6*24
12*12

There are only 8 set of the number that can express N as a product of 2 positive factors

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If N = 144, then what is the number of ways of expressing N as a produ

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If N = 144, then what is the number of ways of expressing N as a produ

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards