You are creating a set of three numbers that have a GCF of 9. You have 27 and 54 for two of the numbers. A. What is the GCF of 27 and 54? B. Find two numbers that you could add to the set of 27 and 54 such that the GCF is now 9.

A. GCF of both is 27

B. By adding 9 and 18 to the set, the GCF of the four numbers become 9

Step-by-step explanation:

A. The GCF of 27 and 54 is 27

GCF represents greatest common factor. It means the highest number which is both a factor of 27 and also a factor of 54. The highest number in this case is 27.

The factors of 27 are ;

1, 3 , 9 , 27

for 54

1,2,3,6,9,18,27 and 54

So we can clearly see that the highest factor in both case is 27

B. Now , we want to add two numbers that will make the GCF to be 9

What about adding 9 and 18?

Let’s have a look;

using the multiples of each;

9 - 1, 3 and 9

18 - 1, 2, 3 , 6 , 9 and 18

27- 1, 3 , 9 and 27

54- 1, 2, 3 , 6, 9, 18, 27 and 54

We can clearly see here that the highest factor that takes all four numbers into consideration is the number 9