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102 LearnersLast updated on September 24, 2025
GCF of 72 and 108
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and schedule events. In this topic, we will learn about the GCF of 72 and 108.
What is the GCF of 72 and 108?
The greatest common factor of 72 and 108 is 36. The largest divisor of two or more numbers is called the GCF of the numbers. 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 108?
To find the GCF of 72 and 108, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 72 and 108 by Using Listing of Factors
Steps to find the GCF of 72 and 108 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 108 = 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108.
Step 2: Now, identify the common factors Common factors of 72 and 108: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Step 3: Choose the largest factor The largest factor that both numbers have is 36.
The GCF of 72 and 108 is 36.
GCF of 72 and 108 Using Prime Factorization
To find the GCF of 72 and 108 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 23 x 32
Prime Factors of 108: 108 = 2 x 2 x 3 x 3 x 3 = 22 x 33
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 3 x 3 = 22 x 32
Step 3: Multiply the common prime factors 22 x 32 = 4 x 9 = 36.
The Greatest Common Factor of 72 and 108 is 36.
GCF of 72 and 108 Using Division Method or Euclidean Algorithm Method
Find the GCF of 72 and 108 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 108 by 72 108 ÷ 72 = 1 (quotient),
The remainder is calculated as 108 − (72×1) = 36
The remainder is 36, not zero, so continue the process
Step 2: Now divide the previous divisor (72) by the previous remainder (36)
Divide 72 by 36 72 ÷ 36 = 2 (quotient), remainder = 72 − (36×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 72 and 108 is 36.
Common Mistakes and How to Avoid Them in GCF of 72 and 108
Finding the GCF of 72 and 108 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 numbers like 10, 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. While it does not affect the GCF, it indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse factors with 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 108 Examples
Problem 1
A chef has 72 apples and 108 oranges. He wants to create fruit baskets with the largest number of fruits in each basket. How many fruits will each basket contain?
We should find the GCF of 72 and 108 GCF of 72 and 108 22 x 32 = 4 x 9 = 36.
There are 36 equal groups 72 ÷ 36 = 2 108 ÷ 36 = 3
There will be 36 groups, and each basket will contain 2 apples and 3 oranges.
Explanation
As the GCF of 72 and 108 is 36, the chef can make 36 baskets.
Now divide 72 and 108 by 36.
Each basket will contain 2 apples and 3 oranges.
Problem 2
A school has 72 red balls and 108 blue balls. They want to arrange them in rows with the same number of balls in each row, using the largest possible number of balls per row. How many balls will be in each row?
GCF of 72 and 108 2^2 x 3^2 = 4 × 9 = 36.
So each row will have 36 balls.
Explanation
There are 72 red and 108 blue balls.
To find the total number of balls in each row, we should find the GCF of 72 and 108.
There will be 36 balls in each row.
Problem 3
A tailor has 72 meters of red fabric and 108 meters of blue fabric. She wants to cut both fabrics 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 108
The GCF of 72 and 108 2^2 x 3^2 = 4 × 9 = 36.
The fabric is 36 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 72 and 108, which is 36.
The length of each piece of fabric will be 36 meters.
Problem 4
A carpenter has two wooden planks, one 72 cm long and the other 108 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 108 22 x 32 = 4 × 9 = 36.
The longest length of each piece is 36 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 72 cm and 108 cm, respectively, we have to find the GCF of 72 and 108, which is 36 cm.
The longest length of each piece is 36 cm.
Problem 5
If the GCF of 72 and ‘b’ is 36, and the LCM is 216, find ‘b’.
The value of ‘b’ is 108.
Explanation
GCF x LCM = product of the numbers
36 × 216 = 72 × b
7776 = 72b
b = 7776 ÷ 72 = 108
FAQs on the Greatest Common Factor of 72 and 108
1.What is the LCM of 72 and 108?
2.Is 72 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 108?
5.Are 72 and 108 prime numbers?
Important Glossaries for GCF of 72 and 108
- Factors: Numbers that divide the target number completely. For example, the factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36.
- Multiple: Products obtained by multiplying a given number by another. For example, the multiples of 6 are 6, 12, 18, 24, and so on.
- Prime Factors: Factors of a number that are prime numbers and divide the given number completely. For example, the prime factors of 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers. For example, the LCM of 72 and 108 is 216.
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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.
