105 LearnersLast updated on August 5th, 2025
GCF of 60 and 72
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 to schedule events. In this topic, we will learn about the GCF of 60 and 72.
What is the GCF of 60 and 72?
The greatest common factor of 60 and 72 is 12. 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 60 and 72?
To find the GCF of 60 and 72, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 60 and 72 by Using Listing of Factors
Steps to find the GCF of 60 and 72 using the listing of factors:
Step 1: Firstly, list the factors of each number:
Factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Factors of 72 = 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.
Step 2: Now, identify the common factors of them.
Common factors of 60 and 72: 1, 2, 3, 4, 6, 12.
Step 3: Choose the largest factor:
The largest factor that both numbers have is 12.
The GCF of 60 and 72 is 12.
GCF of 60 and 72 Using Prime Factorization
To find the GCF of 60 and 72 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 60: 60 = 2 x 2 x 3 x 5 = 22 x 3 x 5
Prime Factors of 72: 72 = 2 x 2 x 2 x 3 x 3 = 23 x 32
Step 2: Now, identify the common prime factors:
The common prime factors are: 2 x 2 x 3 = 22 x 3
Step 3: Multiply the common prime factors:
22 x 3 = 4 x 3 = 12.
The Greatest Common Factor of 60 and 72 is 12.
GCF of 60 and 72 Using Division Method or Euclidean Algorithm Method
Find the GCF of 60 and 72 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 60 72 ÷ 60 = 1 (quotient), The remainder is calculated as 72 − (60×1) = 12
The remainder is 12, not zero, so continue the process
Step 2: Now divide the previous divisor (60) by the previous remainder (12)
Divide 60 by 12 60 ÷ 12 = 5 (quotient), remainder = 60 − (12×5) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 60 and 72 is 12.
Common Mistakes and How to Avoid Them in GCF of 60 and 72
Finding the GCF of 60 and 72 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 60, students may mention 25 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 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 60 and 72 Examples
Problem 1
A chef has 60 apples and 72 oranges. She wants to pack them into the largest possible equal sets. How many pieces of fruit will be in each set?
We should find the GCF of 60 and 72 GCF of 60 and 72
22 x 3 = 4 x 3 = 12.
There are 12 equal sets
60 ÷ 12 = 5
72 ÷ 12 = 6
There will be 12 sets, and each set gets 5 apples and 6 oranges.
Explanation
As the GCF of 60 and 72 is 12, the chef can make 12 sets.
Now divide 60 and 72 by 12.
Each set gets 5 apples and 6 oranges.
Problem 2
A gardener has 60 red roses and 72 yellow roses. He wants to arrange them in bouquets with the same number of roses in each bouquet, using the largest possible number of roses per bouquet. How many roses will be in each bouquet?
GCF of 60 and 72
22 x 3 = 4 × 3 = 12.
So each bouquet will have 12 roses.
Explanation
There are 60 red and 72 yellow roses.
To find the total number of roses in each bouquet, we should find the GCF of 60 and 72.
There will be 12 roses in each bouquet.
Problem 3
A tailor has 60 meters of red fabric and 72 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 60 and 72.
The GCF of 60 and 72
22 x 3 = 4 × 3 = 12.
The fabric is 12 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 60 and 72, which is 12.
The length of each piece of the fabric will be 12 meters.
Problem 4
A carpenter has two wooden planks, one 60 cm long and the other 72 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 60 and 72
22 x 3 = 4 × 3 = 12.
The longest length of each piece is 12 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 60 cm and 72 cm, respectively, we have to find the GCF of 60 and 72, which is 12 cm. The longest length of each piece is 12 cm.
Problem 5
If the GCF of 60 and ‘b’ is 12, and the LCM is 360. Find ‘b’.
The value of ‘b’ is 72.
Explanation
GCF x LCM = product of the numbers
12 × 360 = 60 × b
4320 = 60b
b = 4320 ÷ 60 = 72
FAQs on the Greatest Common Factor of 60 and 72
1.What is the LCM of 60 and 72?
2.Is 60 divisible by 5?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 72?
5.Are 60 and 72 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 60 and 72?
7.What are some fun ways kids in United States can practice GCF of 60 and 72 with numbers?
8.What role do numbers and GCF of 60 and 72 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 60 and 72 skills?
Important Glossaries for GCF of 60 and 72
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- 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 60 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 72 is divided by 5, the remainder is 2 and the quotient is 14.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 60 and 72 is 360.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 60 and 72 is 12, as it is their largest common factor that divides the numbers completely.
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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.
