Question
Find the largest number that, when dividing 259, 323,
and 640, leaves remainders of 4, 8, and 10, respectively.Solution
The required number will divide 255 (259 - 4) , 315 (323 - 8) and 630 (640 - 10) completely.
Now, the greatest number that will divide 255, 315 and 630 completely, is the HCF of these numbers.
255 = 3 X 5 X 17
315 = 32 X 5 X 7
630 = 2 x 32 x 5 x 7
So, HCF of 255, 315 and 630 = 3 x 5 = 15
Therefore, required number is 15.
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