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Q.

The greatest number that will divide 445, 572, and 699, vacating remainders 4, 5, and 6 respectively is ____.


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Detailed Solution

The greatest number that will divide 445, 572, and 699, vacating remainders 4, 5, and 6 respectively is 63.
It is given that the greatest number that will divide 445, 572, and 699 will leave remainders 4, 5, 6 respectively.
Thus we have,
445−4=441 572−5=567 699−6=693 Find the HCF of 441, 567, and 693:
441=3×3×7×7 567=3×3×3×3×7 693=3×3×7×11 ⇒HCF=3×3×7=63 Thus the greatest number that divides 445, 572, and 696, vacating the remainder of 4, 5, and 6 is 63.
 
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