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

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Joined: 02 Sep 2009
Posts: 58402
If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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22 May 2018, 04:30
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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

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Posts: 3074
Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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22 May 2018, 04:52
1
1

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.

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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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22 May 2018, 05:01
Greatest common factor = 12

sum of digits of 12 = 1+2=3
Hence option B = 3 is the answer.
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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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23 May 2018, 00:27
1
A? How? Can we please have the OE?
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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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23 May 2018, 01:05
1
urvashis09 wrote:
A? How? Can we please have the OE?

The OA is B. Edited. Thank you.
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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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30 May 2018, 17:12
Bunuel wrote:
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

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

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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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30 Sep 2018, 07:27
Top Contributor
Bunuel wrote:
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

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

Cheers,
Brent
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Re: If x is the greatest common factor of 36 and 96, what is the sum of  [#permalink]

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30 Sep 2018, 12:40
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

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Re: If x is the greatest common factor of 36 and 96, what is the sum of   [#permalink] 30 Sep 2018, 12:40
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