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The numbers 2604, 1020 and 4812 when divided by a positive integer N

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The numbers 2604, 1020 and 4812 when divided by a positive integer N  [#permalink]

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New post 24 Feb 2020, 04:44
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Question Stats:

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Re: The numbers 2604, 1020 and 4812 when divided by a positive integer N  [#permalink]

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New post 25 Feb 2020, 00:41
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2604-12, 1020-12 and 4812-12 are divisible by N

HCF( 2592, 1008, 4800) = 48


Bunuel wrote:
The numbers 2604, 1020 and 4812 when divided by a positive integer N give the same remainder of 12. What is the greatest possible value of N?

A. 12
B. 24
C. 36
D. 48
E. 96


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Re: The numbers 2604, 1020 and 4812 when divided by a positive integer N  [#permalink]

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New post 29 Mar 2020, 04:59
Bunuel wrote:
The numbers 2604, 1020 and 4812 when divided by a positive integer N give the same remainder of 12. What is the greatest possible value of N?

A. 12
B. 24
C. 36
D. 48
E. 96


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Given: The numbers 2604, 1020 and 4812 when divided by a positive integer N give the same remainder of 12.

Asked: What is the greatest possible value of N?

gcd (2604 - 12, 1020 - 12, 4812 -12) = gcd (2592, 1008, 4800)
2592 = 2*2*2*2*3*3*3*3
1008 = 2*2*2*2*7*3*3
4800 = 2*2*2*2*2*2*3*5*5
gcd (2592, 1008, 4800) = 2*2*2*2*3 = 48

IMO D
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Re: The numbers 2604, 1020 and 4812 when divided by a positive integer N  [#permalink]

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New post 29 Mar 2020, 05:37

Solution



Given
In this question, we are given that
    • The numbers 2604, 1020 and 4812, when divided by a positive integer N, give the same remainder of 12

To find
We need to determine
    • The greatest possible value of N

Approach and Working out
When the given numbers are divided by N, the remainders are 12 every time
    • Hence, (2604 – 12, 1020 – 12, 4812 – 12) must be completely divisible by 12
    • Therefore, the largest number that can divide all 3 = GCD (2592, 1008, 4800) = 48

Thus, option D is the correct answer.

Correct Answer: Option D
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Re: The numbers 2604, 1020 and 4812 when divided by a positive integer N   [#permalink] 29 Mar 2020, 05:37

The numbers 2604, 1020 and 4812 when divided by a positive integer N

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