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What is the greatest common factor of 108, 180, and 810? (A) 6 (B) 9 (

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What is the greatest common factor of 108, 180, and 810? (A) 6 (B) 9 (  [#permalink]

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New post 16 Apr 2020, 09:21
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A
B
C
D
E

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  25% (medium)

Question Stats:

74% (01:21) correct 26% (01:47) wrong based on 31 sessions

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What is the greatest common factor of 108, 180, and 810?

(A) 6

(B) 9

(C) 12

(D) 18

(E) 24
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Joined: 02 Sep 2009
Posts: 64951
Re: What is the greatest common factor of 108, 180, and 810? (A) 6 (B) 9 (  [#permalink]

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New post 16 Apr 2020, 09:28
sjuniv32 wrote:
What is the greatest common factor of 108, 180, and 810?

(A) 6

(B) 9

(C) 12

(D) 18

(E) 24


You can do it in a conventional way or notice that all three numbers are divisible by 9 (the sum of the digits of all three are 9). So, right away the answer is B or D but since all three numbers are even then all three must be divisible by 2*9 = 18 too. Only D fits.

Answer: D.
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Re: What is the greatest common factor of 108, 180, and 810? (A) 6 (B) 9 (  [#permalink]

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New post 16 Apr 2020, 09:53
sjuniv32 wrote:
What is the greatest common factor of 108, 180, and 810?

(A) 6

(B) 9

(C) 12

(D) 18

(E) 24


Observation 1: All numbers i.e. 108, 180, and 810 are even so GCD must be EVEN i.e. Option B Out

Observation 2: Sum of the digits in each number is 9 i.e. they are divisible by 9 i.e. GCD must be a multiple of 9 i.e. Option A C E Out

Answer: Option. D
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Re: What is the greatest common factor of 108, 180, and 810? (A) 6 (B) 9 (   [#permalink] 16 Apr 2020, 09:53

What is the greatest common factor of 108, 180, and 810? (A) 6 (B) 9 (

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