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

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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

⇒ H C F = 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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