Q33 of 56 Page 17

Let d be the H.C.F of 24 and 36. Find two numbers a and b such that d = 24 a + 36 b?

Given, d = H.C.F of 24 and 36

We have 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 …… eq (1)


24 = 2 × 12 + 0


Thus, the H.C.F of 24 and 36 is 12.


From eq (1), we have,


⇒ 12 = 36 – 24


⇒ 12 = 24(–1) + 36(1)


⇒ 12 = 24 a + 36 b, where a = –1 and b = 1


Hence the values are; a = –1 and b = 1


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