M14-04

Question

What is the sum of all common positive factors of 48 and 36?

A. 22
B. 24
C. 26
D. 27
E. 28

Bunuel · Accepted Answer

Official Solution:

What is the sum of all common positive factors of 48 and 36?

A. 22
B. 24
C. 26
D. 27
E. 28

Step 1:  Find the greatest common divisor (GCD) of 48 and 36.
 
• Why start with the GCD? The GCD of two numbers is the largest number that divides both of them without leaving a remainder. As such, all the positive factors of the GCD will also be common factors of the two numbers.
 
The GCD of  48 = 2^4*3  and  36 = 2^2*3^2  is  2^2*3 = 12 .
 
 Step 2:  Find the positive factors of 12.
 
The positive factors are: 1, 2, 3, 4, 6, and 12.
 
 Step 3:  Sum up the factors.
 
 1 + 2 + 3 + 4 + 6 + 12 = 28 .
 
Therefore, the sum of all common positive factors of 48 and 36 is 28.

Answer: E

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

luisdicampo · Answer

Deconstructing the Question  
We are asked to find the sum of all common positive factors of  48  and  36 .

Step-by-step  
Prime factorization:
 48 = 2^4 × 3 
 36 = 2^2 × 3^2

Greatest common divisor:
 GCD = 2^2 × 3 = 12

Common positive factors are the factors of 12:
 1, 2, 3, 4, 6, 12

Sum:
 1 + 2 + 3 + 4 + 6 + 12 = 28

Answer: 28

Jyotsana15 · Answer

I did not quite understand the solution. Why have we calculated GCD and not the LCM?

Bunuel · Answer

This is explained in the solution. In short, once we find the GCD, we only need to list its factors, because any number that divides both original numbers must also divide their GCD.

M14-04

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