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655-705 (Hard)|   Remainders|      
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Bunuel
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The greatest number which can divide 1356, 1868 and 2764 leaving the 01 Jul 2022, 04:15
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

55% (hard)

Question Stats:

71% (02:49) correct 29% (02:47) wrong based on 209 sessions

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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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A
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The greatest number which can divide 1356, 1868 and 2764 leaving the 01 Jul 2022, 08:52
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Back solving where you need to do fast calculations.
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DDB29141-585E-40DB-B18F-7756B2FEC4D1.jpeg
DDB29141-585E-40DB-B18F-7756B2FEC4D1.jpeg [ 143.77 KiB | Viewed 4110 times ]

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The greatest number which can divide 1356, 1868 and 2764 leaving the 01 Jul 2022, 11:37
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Bunuel
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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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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The greatest number which can divide 1356, 1868 and 2764 leaving the 18 Jul 2022, 07:34
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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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The greatest number which can divide 1356, 1868 and 2764 leaving the 06 Jan 2025, 19:54
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The greatest number which can divide 1356, 1868 and 2764 leaving the same remainder 12 in each case

Since, all the numbers are leaving 12 as the remainder so let's start by subtracting 12 from each number.

1356 - 12 = 1344
1868 - 12 = 1856
2764 - 12 = 2752

Now, the number which will decide all these numbers will be the GCD of HCF of these numbers

Attachment:
GCD.jpg
GCD.jpg [ 25.85 KiB | Viewed 1472 times ]

=> All these numbers will be divisible by the GCD which is 4*4*4 = 64

So, Answer will be A
Hope it helps!

Watch the following video to MASTER LCM and GCD

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The greatest number which can divide 1356, 1868 and 2764 leaving the 07 Jan 2025, 00:56
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We can calculate the HCF of 1356, 1868, 2764 by difference method
First Difference
1868- 1356 = 512
2764 - 1868 = 896
Second Difference
896 - 512 = 384
HCF will be the Factor of 384. So 64 X 6 = 384 or
Only 64 can divide 384 in the options. So, Option A is Correct.
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