Question

Find the HCF of 65 and 117 and express it in the form of 65m + 117n.

Answer 1

here is your answer

Answer 2

HCF of 65 and 117 is 13

• HCF of given numbers is the highest common factor of given numbers.
• Finding HCF using Euclid's Division algorithm:
• Statement: If there are two positive integers a and b then there exists two unique integers q and r such that

                         a = bq + r    (0 ≤ r < b)

• Given numbers are 65, 117

            117 = 65 x 1 + 52  ----------------(1)

            65 = 52 x 1 + 13   ----------------(2)    

            52 = 13 x 4 + 0

• Therefore, HCF of 65 and 117 is 13.

• Now, expressing 13 in the form of 65m + 117n

             13 = 65 - 52                             [from (2)]

             13 = 65 - (117 - 65)                   [from (1)]

             13 = 65 - 117 + 65

             13 = 65 x 2 - 117 x 1

             13 = 65 x 2 + 117 x (-1)

             13 = 65m + 117n

                Where m = 2, n = -1