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The greatest number which can divide 1356, 1868 and 2764 leaving the
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Bunuel
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The greatest number which can divide 1356, 1868 and 2764 leaving the [#permalink] New post  01 Jul 2022, 03:15
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What is the greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case?

(A) 64
(B) 124
(C) 156
(D) 260
(E) 312
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Re: The greatest number which can divide 1356, 1868 and 2764 leaving the [#permalink] New post  01 Jul 2022, 07:52
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ThatDudeKnows
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Re: The greatest number which can divide 1356, 1868 and 2764 leaving the [#permalink] New post  01 Jul 2022, 10:37
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Bunuel wrote:
What is the greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case?

(A) 64
(B) 124
(C) 156
(D) 260
(E) 312


We need the greatest common factor of 1344, 1856, and 2752.
1344: 2^6*3*7
1856: 2^6*29
2764: 2^6*43

GCF is 2^6 = 64

Answer choice A.
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ishwan
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Re: The greatest number which can divide 1356, 1868 and 2764 leaving the [#permalink] New post  18 Jul 2022, 06:34
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Subtract 12 from each of the three numbers 1356,1868 and 2764 . We get the numbers that is completely divisible by the divisor . 1356 - 12 = 1344 , 1868 -12 = 1844 and 2764-12 = 2752 . Now determine the GCF of 1344 , 1856 and 2752 . While taking LCM start with 8 or 16 if you are comfortable with it . You will get 64 as the answer.
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