Question

How do you find the greatest common factor of two numbers?

Answer 1

Hint: We take two arbitrary numbers. We need to find the GCF of 21 and 14. 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 solution:
We take two arbitrary numbers 14 and 21 to understand the concept of GCD better.
We need to find the GCF of 21 and 14. GCF stands for greatest common factor.
we first find the factors for 14 and 21.
The factors of 14 are $1,2,7,14$. The factors of 21 are $1,3,7,21$.
The common factors of 14 and 21 are $1,7$.
The greatest common factor of 14 and 21 is $7$.
We also can use the simultaneous factorisation to find the greatest common factor of 14 and 21.
We have to divide both of them with possible primes which can divide both of them.
\[\begin{align}
  & 7\left| \!{\underline {\,
  14,21 \,}} \right. \\
 & 1\left| \!{\underline {\,
  2,3 \,}} \right. \\
\end{align}\]
The only possible prime being 7. Therefore, the greatest common factor of 14 and 21 is 7.

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.