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102 LearnersLast updated on September 19, 2025
GCF of 72 and 18
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share the items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 72 and 18.
What is the GCF of 72 and 18?
The greatest common factor of 72 and 18 is 18. The largest divisor of two or more numbers is called the GCF of the number. If two numbers are co-prime, they have no common factors other than 1, so their GCF is 1.
The GCF of two numbers cannot be negative because divisors are always positive.
How to find the GCF of 72 and 18?
To find the GCF of 72 and 18, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 72 and 18 by Using Listing of Factors
Steps to find the GCF of 72 and 18 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Factors of 18 = 1, 2, 3, 6, 9, 18.
Step 2: Now, identify the common factors of them Common factors of 72 and 18: 1, 2, 3, 6, 9, 18.
Step 3: Choose the largest factor The largest factor that both numbers have is 18.
The GCF of 72 and 18 is 18.
GCF of 72 and 18 Using Prime Factorization
To find the GCF of 72 and 18 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 72: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
Prime Factors of 18: 18 = 2 × 3 × 3 = 2 × 3²
Step 2: Now, identify the common prime factors
The common prime factors are: 2 × 3² = 2 × 9
Step 3: Multiply the common prime factors 2 × 3² = 2 × 9 = 18.
The Greatest Common Factor of 72 and 18 is 18.
GCF of 72 and 18 Using Division Method or Euclidean Algorithm Method
Find the GCF of 72 and 18 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 72 by 18 72 ÷ 18 = 4 (quotient),
The remainder is calculated as 72 − (18×4) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 72 and 18 is 18.
Common Mistakes and How to Avoid Them in GCF of 72 and 18
Finding GCF of 72 and 18 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by the students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 72, students may mention 5, which is incorrect. To avoid this, students should carefully divide the number and list the factors correctly.
Mistake 2
Choosing the wrong common factor
Students may sometimes select the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and find the greatest one.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. However, it does not affect the GCF, but it tells about the incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students confuse between factors and multiples. In that confusion, sometimes they may write multiples instead of factors. To avoid this confusion, students should know the definitions of multiples and factors clearly.
Mistake 5
Assuming GCF is always an even number
Students may assume that the GCF of two numbers will always be an even number. But it's not true; a GCF can also be an odd number. To avoid this, students should focus on common factors rather than focusing on even and odd numbers.
Greatest Common Factor of 72 and 18 Examples
Problem 1
A chef has 72 apples and 18 pears. He wants to create fruit baskets with the same number of fruits in each basket, using the largest possible number of fruits per basket. How many fruits will be in each basket?
We should find GCF of 72 and 18 GCF of 72 and 18 2 × 3² = 2 × 9 = 18.
There are 18 equal baskets 72 ÷ 18 = 4 18 ÷ 18 = 1
There will be 18 baskets, and each basket gets 4 apples and 1 pear.
Explanation
As the GCF of 72 and 18 is 18, the chef can make 18 baskets.
Now divide 72 and 18 by 18.
Each basket gets 4 apples and 1 pear.
Problem 2
A company has 72 black chairs and 18 white chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 72 and 18 2 × 3² = 2 × 9 = 18.
So each row will have 18 chairs.
Explanation
There are 72 black and 18 white chairs.
To find the total number of chairs in each row, we should find the GCF of 72 and 18.
There will be 18 chairs in each row.
Problem 3
A farmer has 72 meters of fencing for his apple orchard and 18 meters of fencing for his pear orchard. He wants to cut both lengths of fencing into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 72 and 18
The GCF of 72 and 18 2 × 3² = 2 × 9 = 18.
The fencing is 18 meters long.
Explanation
For calculating the longest length of the fencing first we need to calculate the GCF of 72 and 18, which is 18.
The length of each piece of the fencing will be 18 meters.
Problem 4
A carpenter has two wooden planks, one 72 cm long and the other 18 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood GCF of 72 and 18 2 × 3² = 2 × 9 = 18.
The longest length of each piece is 18 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 72 cm and 18 cm, respectively, we have to find the GCF of 72 and 18, which is 18 cm.
The longest length of each piece is 18 cm.
Problem 5
If the GCF of 72 and ‘b’ is 18, and the LCM is 216. Find ‘b’.
The value of ‘b’ is 54.
Explanation
GCF × LCM = product of the numbers
18 × 216 = 72 × b
3888 = 72b
b = 3888 ÷ 72 = 54
FAQs on the Greatest Common Factor of 72 and 18
1.What is the LCM of 72 and 18?
2.Is 72 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 18?
5.Are 72 and 18 prime numbers?
Important Glossaries for GCF of 72 and 18
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 18 are 1, 2, 3, 6, 9, and 18.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 72 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 72 and 18 is 72.
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Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
