Question

Let x. be the HCF of 24 and 36 . Find two number a and b such that x= 24a + 36b

Answer 1

Let,
x=HCF of 24 and 36

To find:a and b such that x=24a+36b
Applying Euclid's Division Lemma to 24 and 36,
We get,
36 = 24×1+12
24 = 2×12+0

Thus,the HCF of 24 and 36 is = x
= 12
From (1),we have
12 = 36-24
=> 12 = 24(-1)+36(1)
=> 24(-1)+36(1) = 12

So,
a = -1 and b = 1