Question

What is the GCF for 54, 72?

Answer 1

Hint: We need to find out the greatest common factor of 54 and 72. We start to solve the problem by writing the factors of the numbers 54 and 72. Then, we find the greatest common factor of both the numbers.

Complete step by step answer:
We need to find the greatest common factor of the numbers 54 and 72. We will be solving the given question by writing the factors of both the numbers and then finding out the greatest common factor of the numbers.
The factor is defined as a number that completely divides another number generating the final remainder of zero.
For Example:
Factors of 8: 1,2,4,8.
Reason: 8 can be expressed as the product of (1,8), (2.4), and vice versa. Thus 1,2,4,8 are the factors of 8.
According to our question,
We need to find out the factors of 54 and 72.
Writing the factors of the number 54,
$\Rightarrow 1\times 54=54$
$\Rightarrow 2\times 27=54$
$\Rightarrow 3\times 18=54$
$\Rightarrow 6\times 9=54$
$\Rightarrow 9\times 6=54$
$\Rightarrow 18\times 3=54$
$\Rightarrow 27\times 2=54$
$\Rightarrow 54\times 1=54$
The factors of 54: 1,2,3,6,9,18,27,54
Writing the factors of the number 72,
$\Rightarrow 1\times 72=72$
$\Rightarrow 2\times 36=72$
$\Rightarrow 3\times 24=72$
$\Rightarrow 4\times 18=72$
$\Rightarrow 6\times 12=72$
$\Rightarrow 8\times 9=72$
$\Rightarrow 9\times 8=72$
$\Rightarrow 12\times 6=72$
$\Rightarrow 18\times 4=72$
$\Rightarrow 24\times 3=72$
$\Rightarrow 36\times 2=72$
$\Rightarrow 72\times 1=72$
The factors of 72: 1,2,3,4,6,8,9,12,18,24,36,72
Now,
We have to find the greatest common factor of 54 and 72.
The common factors of the numbers 54 and 72: 1, 2, 3, 6, 9, 18
From the above, we find that there is no number greater than 18 which is a factor of both 54 and 72. So, 18 is the greatest common factor of 54 and 72.

$\therefore$ The greatest common factor of 54 and 72 is 18.

Note: The given question can be alternatively solved as follows,
We need to express the numbers 54 and 72 as a product of prime numbers.
Writing the same, we get,
$\Rightarrow 54=2\times 3\times 3\times 3$
$\Rightarrow 72=2\times 2\times 2\times 3\times 3$
Now, we need to multiply the common factors of both the numbers to get the GCF of the numbers.
The common factors of 54 and 72 are 2, 3, 3.
$\Rightarrow GCF=2\times 3\times 3$
$\therefore GCF=18$