Question

How do you find GCF of $21$ and $45?$

Answer 1

Hint:As GCF is greatest common divisor of any non-zero number, so in order to determine the value of GCF first prime factorise the numbers given in the question, then the multiplication of common numbers of prime factorisation will be GCF of the given number.
As, if we have to determine GCF of $2$ and $4$
Here, prime factorisation of $2=2\times 1$
And, $4$ will be $=2\times 2$
So, here only $2$ is common in both $2$ and $4$
Hence, GCF will be $2$
Apply this concept to determine the solution of the question.

Complete step by step solution:
As per data given in the question,
As here,
We have to determine the GCF of $21$ and $45$
As, GCF stands for Greatest common divisor,
As the name says, greatest means GCF of two numbers will be the greatest number which divides both the numbers.
In order to determining the GCF of $21$ and $45$
We will prime factorise the given numbers,
As we know that,
In prime factorisation method,
We write the given numbers in the form of multiplication of prime numbers.
So,
Prime factorisation of 21 will be $=3\times 7$
And, in the same way,
Prime factorisation of $45$ will be $=3\times 3\times 5$
As, from the prime factorisation,
We can clearly conclude that,
Only 3 is common in the prime factor of both $21$ and $45$
So,
The value of GCF of $21$ and $45$ will be $3$

Note: While calculating the GCF make sure you are taking only prime numbers for the prime factorisation of a given number.
As the smallest prime number is $2,1$ is not considered as a prime number,
Prime numbers are those numbers which are either divisible by $1$ or itself, means such numbers have only two factors.
When finding the GCF make sure you are multiplying all the individual numbers which are common in the prime factorisation of both the numbers.