Question

How do you find the GCF of 18, 45mn?

Answer 1

Hint:
 We will use the concept of factorization. At first, we will find all the factor of 18 and 45mn, and then we will pick out the common factor from both of them. Then, from the common factor, we will select the factor which is greatest among them and that is the GCF.

Complete step by step answer:
We will first understand the term factor of any number. The factor of any number is those number which completely divides the given number. For example: We will say that factor of 6 is 1, 2, 3, and 6 because these are those number which divide the given number completely and no remained is left.
So, we will first find all the factor of 18, and 45mn before calculating the GCF (Greatest Common Factor.)
So, we will say that the factor of the 18 is {1, 2, 3, 6, 9, 18} because these number divides the 18 completely without leaving any remainder.
Now, we will find the factor of 45mn. We can see that 45mn is the multiple of 45, m, and n.
So, m, and n will also, be the factor of 45mn.
Thus, total factors of 45mn is {1, 3, 5, 9, 15, 45, m, n} as these number divides 45mn completely.
Now, we will select all the common factor of 18, and 45mn which is {1, 3, 9}.
And, we can see that in common factors 9 is the greatest common factor among all.
So, the GCF of 18, 45mn is 9. Hence, 9 is our required answer.

Note:
Students are required to note that when we have the multiple of any number for example: let us say we have a number $ x\times y\times z $ . Since, the number $ x\times y\times z $ is the multiple of three number x, y, z. So, we can say that x, y, and z are the factor of the number $ x\times y\times z $ as it is formed by multiplying all the number x, y, and z