Question

let d be the HCF of 24,36.find the number a and b such that d= 24a + 36b

Answer 1

Solution:-d = HCF of 24 and 36To find : a and b such that d = 24a + 36bApplying Euclid's Division Lemma to 24 and 36, we get36 = 24*1 + 12 ...(1)24 = 2*12 + 0Thus, the HCF of 24 and 36 is 12.From (1), we have,⇒ 12 = 36 - 24⇒ 12 = 24(-1) + 36(1)⇒ 12 = 24a + 36bWhere a = -1 and b = 1