Find the HCF of 65 and 117 and find the pair of integral values of m and n such that HCF =65m+117n
Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
=》Here we are using Euclid's Division Algorithm to find the HCF of 65 and 117.
=》117 = (65 × 1) + 52.
=》65 = (52 × 1) + 13
=》52 = (13 × 4) + 0
=》Therefore, the HCF of 65 and 117 is 13.
=Now to calculate the values of m and n =we need to work as:
=》13 = 65 + 52 × (-1)
=》13 = 65 + [117 + 65 × (-1)] × (-1)
=》13 = 65 + 65 × (-1) x (-1) + 117 × (-1)
=》13 = 65 × 2 + 117 × (-1)
=》Now compare this equation with "HCF = 65m + 117n",
=》Hence, m = 2 and n = -1
=》Therefore, the HCF of 65 and 117 is 13, the values of m and n are: m = 2 and n = -1.