Question

Find the greatest number that will divide 445 572 and 669 leaving remainders 4 5 and 6 respectively

Answer 1

If it was to find the greatest number that would divide these number , the solution can be found by finding HCF .

Here the question demands, on dividing these number ,it leaves reminders .Therefore we substract each numbers with their respective reminders and then calculate the HCF (highest common factor).
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.