Question

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

Answer 1

Hint: As we know that the HCF is the highest common factor i.e the highest common number which divides two or more numbers. Here we will use Euclid’s division lemma to the above question and we will get the answer.

Complete step-by-step answer:

Let us consider the above question we have
d = HCF of 24 and 36
we have to find a and b such that $d=24a+36b$
Now we will apply the Euclid’s division lemma to 24 and 36, we get
\[\begin{align}
  & 36=24(1)+12....................(1) \\
 & 24=2(12)+0 \\
\end{align}\]
Thus the HCF of 24 and 36 is 12.
From the equation (1) we have,
\[\begin{align}
  & \Rightarrow 12=36-24 \\
 & \Rightarrow 12=24(-1)+36(1) \\
 & \Rightarrow 12=24a+36b \\
\end{align}\]
Where a= -1 and b= 1.
Therefore the two numbers a and b are -1 and 1 respectively.

Note: Be careful while doing calculation as there is a chance that you might make mistakes during the calculation and you will get the incorrect answer. Just remember the concept of Euclid’s division lemma as it is very helpful in these types of questions. Also remember the concept of HCF ( highest common factor) and the way to find it. Also remember the fact that a natural number, greater than 1, can always be written as the sum of greatest common divisor and lowest common multiple of two natural numbers.