In this article, I show you 4 methods how to find the greatest common factor of 18 and 48. One of the methods is just three simple steps!
As a high school maths teacher since 2007 I have found that students who know how to find the greatest common factor find other math topics easier.
You can apply these methods to find the greatest common factor (GCF) of any other 2 numbers and use this math skill for other topics like factorizing in algebra and simplifying fractions. Let’s get started!
What is the GCF of 18 and 48?
The GCF of 18 and 48 is 6.
What is the greatest common factor?
The greatest common factor is the largest whole number, which divides exactly into 2 (or more) numbers without any remainder.
The greatest common factor (GCF) is also known as the highest common factor (HCF) or greatest common divisor (GCD).
How to find the GCF of 18 and 48
We can find the GCF of 18 and 48 using these methods:
- common factor method
- prime factorization method
- Euclid’s algorithm method
- Calculator method
Common factor method
Step 1: Find the factors of 18
The factors of 18 are 1, 2, 3, 6, 9, 18.
You can find the factors of 18 using the methods outlined in this article.
Step 2: Find the factors of 48
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Step 3: Find the common factors of 18 and 48
The common factors of 18 & 48 are 1, 2, 3 & 6.
Step 4: Identify the highest common factor
Out of these common factors the greatest common factor is 6.
Prime factorization method
Step 1: Find the prime factorization of 18
18 = 2 x 3 x 3
This can be found by drawing a factor tree to find the prime factors of 18
Step 2: Find the prime factorization of 48
48 = 2 x 2 x 2 x 2 x 3
Step 3: Multiply the common prime factors
The common prime factors of 18 & 48 are 2 and 3.
2 x 3 = 6
Therefore the highest common factor of 18 & 48 is 6.
Euclid’s Algorithm method
This is an efficient method to find the greatest common divisor of two numbers. It is also referred to as the Euclidean division lemma.
This method can be written out as a process of long division and repeated subtraction, but at its core, it’s finding how many times one number goes into another until you hit zero.
A detailed explanation of Euclid’s Algorithm method can be found here.
Calculator method
On some scientific calculators such as the Casio fx 82 AU PLUS II or the Casio fx-100AU you can enter any 2 numbers and it will find the GCF for you.
This short video shows you how to do this.
GCF of 18 and 48 Examples
Question: What is the highest common factor of 18abc and 48a2b?
Solution: 6ab
Question: Factorize 18x + 48xy
Solution: Take the GCF of both terms, 6x, out the front of the brackets to get 6x(3+8y)
Question: Simplify the fraction 18/48
Solution: Divide both the numerator and denominator by the GCF of 6 to get 3/8
Question: Simplify the ratio 18:48
Solution: Divide both numbers by the GCF of 6 to get 3:8
FAQs on GCF of 18 and 48
What is the GCF of 18, 36 & 48?
The GCF of 18, 36 & 48 is 6 because the common prime factors are 2 & 3, and when multiplied they give 6 the greatest common factor.
How to find the GCF of 3 numbers
To find the greatest common factor of three numbers you can list out the common factors and identify the greatest one.
Another method is to use prime factorization as shown in this article. Multiply the common prime factors.
What is the greatest common multiple of 18 and 48?
The greatest common multiple of 18 and 48 is 144. To find the greatest common multiple, list out the multiples of each number and identify the smallest one that appears in both lists:
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144
Multiples of 48: 48, 96, 144, 192, 240
GCF of prime numbers
The GCF of 2 or more prime numbers is always 1 since a prime number only has 2 factors 1 and itself.
Final thoughts on How to Find the Greatest Common Factor of 18 and 48 in 3 simple steps
Finding the greatest common factor or greatest common divisor of two numbers is a helpful mathematical skill to have.
If you want to find the greatest common factor or greatest common divisor, there are a few different ways to go about it.
Practice these methods with some friends or fellow students so you can get better at identifying GCFs in no time!
