104 LearnersLast updated on August 5th, 2025
GCF of 72 and 120
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 schedule events. In this topic, we will learn about the GCF of 72 and 120.
What is the GCF of 72 and 120?
The greatest common factor of 72 and 120 is 24. 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 120?
To find the GCF of 72 and 120, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 72 and 120 by Using Listing of Factors
Steps to find the GCF of 72 and 120 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 120 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
Step 2: Now, identify the common factors of them Common factors of 72 and 120: 1, 2, 3, 4, 6, 8, 12, 24.
Step 3: Choose the largest factor
The largest factor that both numbers have is 24.
The GCF of 72 and 120 is 24.
GCF of 72 and 120 Using Prime Factorization
To find the GCF of 72 and 120 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 = 2^3 x 3^2
Prime Factors of 120: 120 = 2 x 2 x 2 x 3 x 5 = 2^3 x 3 x 5
Step 2: Now, identify the common prime factors
The common prime factors are: 2 x 2 x 2 x 3 = 2^3 x 3
Step 3: Multiply the common prime factors 2^3 x 3 = 8 x 3 = 24.
The Greatest Common Factor of 72 and 120 is 24.
GCF of 72 and 120 Using Division Method or Euclidean Algorithm Method
Find the GCF of 72 and 120 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 120 by 72 120 ÷ 72 = 1 (quotient),
The remainder is calculated as 120 − (72×1) = 48
The remainder is 48, not zero, so continue the process
Step 2: Now divide the previous divisor (72) by the previous remainder (48)
Divide 72 by 48 72 ÷ 48 = 1 (quotient), remainder = 72 − (48×1) = 24
Step 3: Now divide the previous divisor (48) by the previous remainder (24) 48 ÷ 24 = 2 (quotient), remainder = 48 − (24×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 72 and 120 is 24.
Common Mistakes and How to Avoid Them in GCF of 72 and 120
Finding the GCF of 72 and 120 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 7, 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 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 120 Examples
Problem 1
A gardener has 72 tulips and 120 daisies. She wants to make equal bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 72 and 120 GCF of 72 and 120 2^3 x 3 = 8 x 3 = 24.
There are 24 equal bouquets 72 ÷ 24 = 3
120 ÷ 24 = 5
There will be 24 bouquets, and each bouquet gets 3 tulips and 5 daisies.
Explanation
As the GCF of 72 and 120 is 24, the gardener can make 24 bouquets. Now divide 72 and 120 by 24. Each bouquet gets 3 tulips and 5 daisies.
Problem 2
A school has 72 red chairs and 120 blue 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 120 2^3 x 3 = 8 × 3 = 24.
So each row will have 24 chairs.
Explanation
There are 72 red and 120 blue chairs. To find the total number of chairs in each row, we should find the GCF of 72 and 120. There will be 24 chairs in each row.
Problem 3
A tailor has 72 meters of red fabric and 120 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 120
The GCF of 72 and 120
2^3 x 3 = 8 × 3 = 24.
The fabric is 24 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 72 and 120, which is 24. The length of each piece of the fabric will be 24 meters.
Problem 4
A carpenter has two wooden boards, one 72 cm long and the other 120 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 120
2^3 x 3 = 8 × 3 = 24.
The longest length of each piece is 24 cm.
Explanation
To find the longest length of each piece of the two wooden boards, 72 cm and 120 cm, respectively, we have to find the GCF of 72 and 120, which is 24 cm. The longest length of each piece is 24 cm.
Problem 5
If the GCF of 72 and 'b' is 24, and the LCM is 360. Find 'b'.
The value of 'b' is 120.
Explanation
GCF x LCM = product of the numbers 24 × 360 = 72 × b
8640 = 72b
b = 8640 ÷ 72 = 120
FAQs on the Greatest Common Factor of 72 and 120
1.What is the LCM of 72 and 120?
2.Is 72 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 120?
5.Are 72 and 120 prime numbers?
6.How can children in Vietnam use numbers in everyday life to understand GCF of 72 and 120?
7.What are some fun ways kids in Vietnam can practice GCF of 72 and 120 with numbers?
8.What role do numbers and GCF of 72 and 120 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve GCF of 72 and 120 skills?
Important Glossaries for GCF of 72 and 120
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 5 are 5, 10, 15, 20, 25, 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 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 72 and 120 is 360.
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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.
