Question

Find the HCF of 36 and 45 by short division method.

Answer 1

Hint: We need to find the HCF of 36 and 45. First we need to find the common factors of 14 and 21 from their factors’ list. Then we find the greatest common factor of 14 and 21. We can also take the simultaneous factorisation of those two numbers to find the GCF.

Complete step-by-step answer:
We need to find the HCF of 36 and 45. GCF stands for highest common factor.
We can use the simultaneous factorisation to find the highest common factor of 36 and 45. It is also known as a short-division method.
We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 3\left| \!{\underline {\,
  36,45 \,}} \right. \\
 & 3\left| \!{\underline {\,
  12,15 \,}} \right. \\
 & 1\left| \!{\underline {\,
  4,5 \,}} \right. \\
\end{align}\]
The possible primes being 3 and 3. Therefore, the greatest common factor of 36 and 45 is $3\times 3=9$.
we first find the factors for 36 and 45.
The factors of 36 are $1,2,3,4,6,9,12,18,36$. The factors of 45 are $1,3,5,9,15,45$.
The common factors of 36 and 45 are $1,3,9$.
The greatest common factor of 36 and 45 is 9.
So, the correct answer is “9”.

Note: We need to remember that the GCF has to be only one number. It is the greatest possible divisor of all the given numbers. If the given numbers are prime numbers then the GCD of those numbers will always be 1.
Therefore, if for numbers $x$ and $y$, the GCD is $a$ then the GCD of the numbers $\dfrac{x}{a}$ and $\dfrac{y}{a}$ will be 1.