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The greatest common factor of 16 and the positive integer n is 4, and
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18 May 2021, 01:04
18 May 2021, 01:04
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The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 210?
A. 3
B. 14
C. 30
D. 42
E. 70
A. 3
B. 14
C. 30
D. 42
E. 70
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Schools: XLRI Jamshedpur, India - Class of 2014
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The greatest common factor of 16 and the positive integer n is 4, and
[#permalink]
18 May 2021, 20:08
18 May 2021, 20:08
1
The greatest common factor of 16 and the positive integer n is 4
=> n and 16 have 4 as their factors
=> n is a multiple of 4 and can be a multiple of some other number which does not have any common factor with 16
=> n is a multiple of 4 and can be a multiple of any other odd number or numbers ...(1)
The greatest common factor of n and 45 is 3
=> n and 45 have 3 as their factors
=> n is a multiple of 3 and can be a multiple of some other number which does not have any common factor with 45 ...(2)
Combining (1) and (2) we get n has 3 and 4 as its factors
=> n is a multiple of 3 and 4 => n is a multiple of 12 => n = 12k
GCD(n,210)
=> GCD(12k,210)
Now 12 and 210 have only 6 common but 6 is not there in the answer choice. So we will look for multiples of 6 and see which are possible
Only C and D are possible
C is 30 but n cannot have 5 as its factor because n and 45 have only 3 common
So, Answer will be D
Hope it helps!
To learn more about LCM and GCD watch the following videos
=> n and 16 have 4 as their factors
=> n is a multiple of 4 and can be a multiple of some other number which does not have any common factor with 16
=> n is a multiple of 4 and can be a multiple of any other odd number or numbers ...(1)
The greatest common factor of n and 45 is 3
=> n and 45 have 3 as their factors
=> n is a multiple of 3 and can be a multiple of some other number which does not have any common factor with 45 ...(2)
Combining (1) and (2) we get n has 3 and 4 as its factors
=> n is a multiple of 3 and 4 => n is a multiple of 12 => n = 12k
GCD(n,210)
=> GCD(12k,210)
Now 12 and 210 have only 6 common but 6 is not there in the answer choice. So we will look for multiples of 6 and see which are possible
Only C and D are possible
C is 30 but n cannot have 5 as its factor because n and 45 have only 3 common
So, Answer will be D
Hope it helps!
To learn more about LCM and GCD watch the following videos
gmatclubot
The greatest common factor of 16 and the positive integer n is 4, and [#permalink]
18 May 2021, 20:08
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