Question

Use euclid division algorithm .find the largest number which divides the 450,577,704 leaving remainder 9,10,11 respectively

Answer 1

63 is larger number which divides the 450,577,704 leaving remainder 9,10,11 respectively

Step-by-step explanation:

• Given that three number

        450,577 and 704

• After divide by highest divisor leave remainder 9, 10 and 11

        So we have to find out H.C.M of (450-9), (577-10), (704-11)

        Means

        H.C.M of 441, 567, 693

• It can be solved by Euclid division algorithm method

        Which is a =bq +r     where  0 ≤ r < b

• First consider 567 and 693 use Euclid division algorithm method

        693 = 1×567 + 126

        567 = 4×126 +63

        126 = 2×63 +0

        So H.C.M of 567 and 693 is 63

• Now consider 441 and 63 use Euclid division algorithm method

         441 = 7×63 +0

        So H.C.M of 441 and 63 is 63

• We see that H.C.M of 441, 567, 693 is 63
• Means 63 is larger number which divides the 450,577,704 leaving remainder 9,10,11 respectively

Answer 2

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