Question

How do we find the GCF of 2 and 14 ?

Answer 1

Hint: In this question we have been told to find the GCF of the two given numbers. GCF stands for greatest common factor and is the number which is a factor for both the numbers and also is the greatest out of all the possible factors. We will express both the numbers as a product of their prime factors and pick the factor which is common in both and is also the greatest to get the required solution.

Complete step-by-step solution:
The given numbers are $2$ and $14$.
Now the factors of $2$ are all the prime numbers between $1$ and $2$ which divide $2$ evenly without any remainder.
Now we know that $2$ is a prime number therefore the only factor left for the number $2$is $1$.
Therefore, we can write $2$ as:
$\Rightarrow 2=2\times 1$
Now the factors of $14$ are all the prime numbers between $1$ and $14$ which divide $14$ evenly without any remainder.
Now $14$ can be written as a product of its constituent prime numbers as:
$\Rightarrow 14=2\times 7$
Now on writing the factored numbers together, we get:
$\Rightarrow 2=2\times 1$
$\Rightarrow 14=2\times 1\times 7$
Now the factor which is common to both the numbers is $2$.
Since there is no other factor which is greater than $2$, the GCF is $2$.
Therefore, the GCF of $2$ and $14$ is, which is the required answer.

Note: The greatest common factor of numbers is used for simplification purposes in an equation.
It is to be remembered that for a number,$1$ and the number itself will be the factors of that number.
There also exists the LCM which stands for the lowest common multiple which is the lowest multiple which two or more numbers have in common. The LCM is used to simplify fractions.