If x is the greatest common factor of 36 and 96, what is the sum of

Question

If x is the greatest common factor of 36 and 96, what is the sum of the digits of x?

A. 2
B. 3
C. 4
D. 6
E. 9

EgmatQuantExpert · Answer

Solution

Given:  
• In the question, x is defined as the greatest common factor of 36 and 96

To find:  
• The sum of the digits of x

Approach and Working:   
• Let’s factorise the numbers 36 and 96 first:
 o 36 =  2^2 * 3^2 
o 96 =  2^5 * 3  
• Therefore, the greatest common factor of 36 and 96 =  2^2 * 3  = 12
• Sum of the digits of 12 = 1 + 2 = 3

Hence, the correct answer is option B.

Answer: B

houston1980 · Answer

Greatest common factor = 12

sum of digits of 12 = 1+2=3
Hence  option B = 3   is the answer.

US09 · Answer

A? How? Can we please have the OE?

Bunuel · Answer

The OA is B. Edited. Thank you.

JeffTargetTestPrep · Answer

Since 12 is the largest number that divides both 36 and 96, 12 is the GCF. The sum of the digits is 3.

Answer: B

BrentGMATPrepNow · Answer

Payal's solution is the approach I'd take, but another way to answer this question is to simply  LIST the factors  of each value and then find the GREATEST factor they have in common.

When listing factors, it's best to do so  in pairs  of values with a given product (either 36 or 96). Here's what I mean:

Factors of 36 = {1, 36}
= {1, 2, 18, 36}
= {1, 2, 3, 12, 18, 36}
= {1, 2, 3, 4, 9, 12, 18, 36}
= {1, 2, 3, 4, 6, 9,  12 , 18, 36}

Following the same approach, we see that the factors of 96 are {1, 2, 3, 4, 6, 8,  12 , 16, 24, 32, 48, 96}

When we examine both sets of factors, we see that the greatest common factor is  12  (i.e., x =  12 )

What is the sum of the digits of x?  
 1  +  2  = 3

Answer: B

Cheers,
Brent

Salsanousi · Answer

Another approach would be

36 96 both divided by 2

18 48 divided by 2 again

9 and 24 divided by 3
3 and 8 we stop here as we have nothing in common.

So 2 * 2 * 3 = 12

1 + 2 = 3

Answer choice B

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If x is the greatest common factor of 36 and 96, what is the sum of

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If x is the greatest common factor of 36 and 96, what is the sum of

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