Question

How do you find the greatest common factor of $ 12 $ and $ 18 $ ?

Answer 1

Hint: In this question, we need to determine the Greatest Common Factor (GCF) of $ 12 $ and $ 18 $ . Here, we will use the prime factorization method to determine the prime factors of $ 12 $ and $ 18 $ . Then, from that we will find the common factors and multiply them to get the GCF of $ 12 $ and $ 18 $ .

Complete step-by-step answer:
Here, we need to find the GCF $ 12 $ and $ 18 $ .
First, we are going to determine the prime factorization of both the given numbers.
Prime factorization is a method of finding prime numbers which multiply to make the original number.
Now, let us determine the prime factorization of $ 12 $ ,
 $ 12 = 2 \times 2 \times 3 $
Now, let us determine the prime factorization of $ 18 $ ,
 $ 18 = 2 \times 3 \times 3 $
So, from the prime factorization of both the numbers, we can say that the common factors of both the numbers are $ 2 $ and $ 3 $ .
Therefore, to determine the GCF of both the given numbers, we need to multiply the common factors of $ 12 $ and $ 18 $.
Thus, GCF $ = 2 \times 3 $ $ = 6 $
Hence, the GCF of $ 12 $ and $ 18 $ is $ 6 $ .
So, the correct answer is “6”.

Note: In this question it is important to note that the Greatest Common Factor (GCF) is the greatest number that will divide both $ 12 $ and $ 18 $ . In other words, it is the number that contains all the factors common to both numbers. The Greatest Common Factor (GCF) is also known as Greatest Common Divisor (GCD) or Highest Common Factor (HCF). We have another method for finding the GCF, which is called ‘listing’. In that method we will list the multiples of both the given numbers until we find the first duplicate. But, this method is awful for the greatest numbers.