Let “d” be the HCF of 24 and 36. Find two numbers a and b such that d = 24a + 36b

Let “d” be the HCF of 24 and 36. Find two numbers a and b such that d=24a+36b.

Answer: The two numbers a and b are -1 and 1 respectively.

Explanation:

The highest common factor (HCF) is the highest common number that divides two or more numbers, as we all know. We shall use Euclid’s division lemma to the given problem and obtain the solution.

Step-by-step instructions:

In the given question, we have d = HCF of 24 and 36.

Applying the Euclid’s division lemma to 24 and 36, we obtain

36 = 24(1) +12     (1)

24 = 2(12) +0

Therefore, HCF of 24 and 36 is 12.

From first equation, we get,

12 = 36−24

12 = 24(−1) + 36(1)

12 = 24a + 36b

So, a = -1 and b = 1.