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Question

Find the greatest number that will divide 445, 572 and 699 leaving remainder 4,5,6 effectively


Solution

Solution-> 445 - 4 = 441 
                 572 - 5 = 567 
                 699 - 6 = 693 

Now find the greatest common factor of those 3 numbers: 
441 = 3 x 3 x 7 x 7 
572 = 3 x 3 x 3 x 3 x 7 
693 = 3 x 3 x 7 x 11 

The common factors are 3 x 3 x 7 = 63 
HCF Of (441,567,693) = 63 

445 / 63 = 7 remainder 4 
572 / 63 = 9 remainder 5 
699 / 63 = 11 remainder 6 

Answer: 
63 is the largest divisor that will give the desired remainders.

 

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