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103 LearnersLast updated on 11 August 2025
GCF of 81 and 72
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 81 and 72.
What is the GCF of 81 and 72?
The greatest common factor of 81 and 72 is 9. 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 81 and 72?
To find the GCF of 81 and 72, a few methods are described below - Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 81 and 72 by Using Listing of factors
Steps to find the GCF of 81 and 72 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 81 = 1, 3, 9, 27, 81.
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 81 and 72: 1, 3, 9.
Step 3: Choose the largest factor The largest factor that both numbers have is 9. The GCF of 81 and 72 is 9.
GCF of 81 and 72 Using Prime Factorization
To find the GCF of 81 and 72 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 81: 81 = 3 x 3 x 3 x 3 = 34
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: 3 x 3 = 32
Step 3: Multiply the common prime factors 32 = 3 x 3 = 9.
The Greatest Common Factor of 81 and 72 is 9.
GCF of 81 and 72 Using Division Method or Euclidean Algorithm Method
Find the GCF of 81 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 81 by 72 81 ÷ 72 = 1 (quotient), The remainder is calculated as 81 − (72×1) = 9
The remainder is 9, not zero, so continue the process
Step 2: Now divide the previous divisor (72) by the previous remainder (9) Divide 72 by 9 72 ÷ 9 = 8 (quotient), remainder = 72 − (9×8) = 0
The remainder is zero, so the divisor will become the GCF. The GCF of 81 and 72 is 9.
Common Mistakes and How to Avoid Them in GCF of 81 and 72
Finding the GCF of 81 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 81, students may mention 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. However, it does not affect the GCF, but 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 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 that 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 81 and 72 Examples
Problem 1
A chef has 81 apples and 72 oranges. She wants to make fruit baskets with an equal number of each fruit in each basket. What is the largest number of baskets she can make?
We should find the GCF of 81 and 72 GCF of 81 and 72 3^2 = 3 x 3 = 9. There are 9 equal baskets 81 ÷ 9 = 9 72 ÷ 9 = 8 There will be 9 baskets, and each basket gets 9 apples and 8 oranges.
Explanation
As the GCF of 81 and 72 is 9, the chef can make 9 baskets. Now divide 81 and 72 by 9. Each basket gets 9 apples and 8 oranges.
Problem 2
An event organizer has 81 red flags and 72 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 81 and 72 3^2 = 3 x 3 = 9. So each row will have 9 flags.
Explanation
There are 81 red and 72 blue flags. To find the total number of flags in each row, we should find the GCF of 81 and 72. There will be 9 flags in each row.
Problem 3
A gardener has 81 meters of red hose and 72 meters of blue hose. She wants to cut both hoses 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 81 and 72 The GCF of 81 and 72 3^2 = 3 x 3 = 9. The hose is 9 meters long.
Explanation
For calculating the longest length of the hose first, we need to calculate the GCF of 81 and 72, which is 9. The length of each piece of the hose will be 9 meters.
Problem 4
A carpenter has two wooden planks, one 81 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 81 and 72 3^2 = 3 x 3 = 9. The longest length of each piece is 9 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 81 cm and 72 cm, respectively. We have to find the GCF of 81 and 72, which is 9 cm. The longest length of each piece is 9 cm.
Problem 5
If the GCF of 81 and ‘a’ is 9, and the LCM is 648. Find ‘a’.
The value of ‘a’ is 72.
Explanation
GCF x LCM = product of the numbers 9 × 648 = 81 × a 5832 = 81a a = 5832 ÷ 81 = 72
FAQs on the Greatest Common Factor of 81 and 72
1.What is the LCM of 81 and 72?
2.Is 81 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 72?
5.Are 81 and 72 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 81 and 72?
7.What are some fun ways kids in United Kingdom can practice GCF of 81 and 72 with numbers?
8.What role do numbers and GCF of 81 and 72 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve GCF of 81 and 72 skills?
Important Glossaries for GCF of 81 and 72
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- 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.
- Euclidean Algorithm: A method for finding the greatest common divisor of two numbers by dividing and replacing until the remainder is zero.
- 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.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 81 and 72 is 648.
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.
