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Question
Find the greatest number that will divide 445, 572 and 699 leaving remainders 4, 5 and 6 respectively.
Solution
The required number when divides 445, 572 and 699 leaves remainders 4, 5 and 6
This means 445 – 4 = 441, 572 – 5 = 561 and 699 – 6 = 693 are completely divisible by the number
∴ The required number = HCF of 441, 567 and 693
First consider 441 and 567
By applying Euclid’s division lemma
567 = 441 × 1 + 126
441 = 126 × 3 + 63
126 = 63 × 2 + 0
∴ HCF of 441 and 567 = 63
Now consider 63 and 693
By applying Euclid’s division lemma
693 = 63 × 11 + 0
∴ HCF of 441, 567 and 693 = 63
Hence required number is 63
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