Question

What is the GCF OF 60 and 45?

Answer 1

Hint: Greatest common factor means the greatest number that is factor of both the given numbers. So, to find the GCF of given two numbers, write all the factors of given two numbers and then find the greatest common factor from them.

Complete step-by-step solution:
In this question, we are given 2 numbers 60 and 45 and we need to find their greatest common factor.
Now, first of all what is GCF?
GCF is the greatest common factor which is the greatest number that is common and divides the given 2 numbers without leaving remainder. For example: 4 and 8. Now, factors of 4 are 1, 2, 4. And the factors of 8 are 1, 2, 4, 8. Therefore, the greatest number that is a factor of both these numbers is 4. Hence, the GCF of 4 and 8 is 4.
Here, we have to find the greatest number that divides 45 and 60.
Finding GCF using Factors:
First write the factors of 45.
$ \Rightarrow $Factors of 45$ = 1,3,5,9,15,45$
Now, write the factors of 60.
$ \Rightarrow $Factors of 60$ = 1,2,3,4,5,6,10,12,15,20,30,60$
Here, we can see that the greatest common factor between 45 and 60 is 15.
Hence, the GCF of 45 and 60 is 15.

Note: We can also find the GCF of 45 and 60 using the prime factorization method.
Write down the prime factors of 45 and 60.
$ \Rightarrow $Prime factors of 45$ = 3 \times 5 \times 3$
$ \Rightarrow $Prime factors of 60$ = 2 \times 2 \times 3 \times 5$
Here, Common factors$ = 3,5$
Therefore, GCF of 45 and 60$ = 3 \times 5 = 15$.