110 LearnersLast updated on August 5th, 2025
GCF of 27 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 to schedule events. In this topic, we will learn about the GCF of 27 and 72.
What is the GCF of 27 and 72?
The greatest common factor of 27 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 27 and 72?
To find the GCF of 27 and 72, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 27 and 72 by Using Listing of Factors
Steps to find the GCF of 27 and 72 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 27 = 1, 3, 9, 27.
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 27 and 72: 1, 3, 9.
Step 3: Choose the largest factor The largest factor that both numbers have is 9.
The GCF of 27 and 72 is 9.
GCF of 27 and 72 Using Prime Factorization
To find the GCF of 27 and 72 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 27: 27 = 3 x 3 x 3 = 3³
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 = 9.
The Greatest Common Factor of 27 and 72 is 9.
GCF of 27 and 72 Using Division Method or Euclidean Algorithm Method
Find the GCF of 27 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 27 72 ÷ 27 = 2 (quotient),
The remainder is calculated as 72 − (27×2) = 18
The remainder is 18, not zero, so continue the process
Step 2: Now divide the previous divisor (27) by the previous remainder (18)
Divide 27 by 18 27 ÷ 18 = 1 (quotient), remainder = 27 − (18×1) = 9
Step 3: Now divide the previous divisor (18) by the previous remainder (9)
Divide 18 by 9 18 ÷ 9 = 2 (quotient), remainder = 18 − (9×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 27 and 72 is 9.
Common Mistakes and How to Avoid Them in GCF of 27 and 72
Finding the GCF of 27 and 72 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 27, 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 demonstrates 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 27 and 72 Examples
Problem 1
A teacher has 27 notebooks and 72 pens. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find the GCF of 27 and 72 GCF of 27 and 72 3² = 9.
There are 9 equal groups.
27 ÷ 9 = 3
72 ÷ 9 = 8
There will be 9 groups, and each group gets 3 notebooks and 8 pens.
Explanation
As the GCF of 27 and 72 is 9, the teacher can make 9 groups.
Now divide 27 and 72 by 9.
Each group gets 3 notebooks and 8 pens.
Problem 2
A school has 27 red apples and 72 green apples. They want to arrange them in rows with the same number of apples in each row, using the largest possible number of apples per row. How many apples will be in each row?
GCF of 27 and 72 3² = 9. So each row will have 9 apples.
Explanation
There are 27 red and 72 green apples.
To find the total number of apples in each row, we should find the GCF of 27 and 72.
There will be 9 apples in each row.
Problem 3
A tailor has 27 meters of silk ribbon and 72 meters of cotton ribbon. She wants to cut both ribbons 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 27 and 72
The GCF of 27 and 72 3² = 9.
The ribbon is 9 meters long.
Explanation
For calculating the longest length of the ribbon, first, we need to calculate the GCF of 27 and 72, which is 9. The length of each piece of the ribbon will be 9 meters.
Problem 4
A carpenter has two wooden planks, one 27 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 27 and 72 3² = 9.
The longest length of each piece is 9 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 27 cm and 72 cm, respectively, we have to find the GCF of 27 and 72, which is 9 cm. The longest length of each piece is 9 cm.
Problem 5
If the GCF of 27 and ‘b’ is 9, and the LCM is 216. Find ‘b’.
The value of ‘b’ is 72.
Explanation
GCF x LCM = product of the numbers
9 × 216 = 27 × b
1944 = 27b
b = 1944 ÷ 27 = 72
FAQs on the Greatest Common Factor of 27 and 72
1.What is the LCM of 27 and 72?
2.Is 27 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 72?
5.Are 27 and 72 prime numbers?
6.How can children in Canada use numbers in everyday life to understand GCF of 27 and 72?
7.What are some fun ways kids in Canada can practice GCF of 27 and 72 with numbers?
8.What role do numbers and GCF of 27 and 72 play in helping children in Canada develop problem-solving skills?
9.How can families in Canada create number-rich environments to improve GCF of 27 and 72 skills?
Important Glossaries for GCF of 27 and 72
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- 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, 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 3².
- 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 27 and 72 is 216.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 27 and 72 will be 9, 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.
