Question

Let d be the HCF of 24 and 36.find any two numbers a and b in such that d = 24 a + 36 b.

Answer 1

Solution:-
d = H.C.F. of 24 and 36
To find: a and b such that :- d = 24a + 36b
Applying Euclid's division lemma to 24 and 36, we get
36 = 24 × 1 + 12 .....(1)
24 = 2 × 12 + 0 .......(2)
So, 12 is the H.C.F. of 24 and 36
From (1), we have,
⇒ 12 = 36 - 24
⇒ 12 = 24(-1) + 36(1)
⇒ 12 = 24a + 36b
wherea = -1 and b = 1   Answer.