Question

14. If HCF (35,115)= 35m+115n, then m + n is

Answer 1

value of (m + n) = -9

HCF of 35 and 115 = 35m + 115n

we have to find out (m + n)

first find HCF of 35 and 115,

prime factors of 35 = 1 × 5 × 7

prime factors of 115 = 1 × 5 × 23

now common factors = 1 × 5

hence highest common factor (HCF) = 1 × 5 = 5

now 5 = 35m + 115n

⇒1 = 7m + 23n

if we take, m = -13 and n = 4

7(-13) + 23 × 4 = -91 + 92 = 1 (satisfied)

hence m + n = -13 + 4 = -9

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