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104 LearnersLast updated on September 20, 2025
GCF of 72 and 39
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 39.
What is the GCF of 72 and 39?
The greatest common factor of 72 and 39 is 3. 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 39?
To find the GCF of 72 and 39, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 72 and 39 by Using Listing of Factors
Steps to find the GCF of 72 and 39 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 39 = 1, 3, 13, 39.
Step 2: Now, identify the common factors of them Common factors of 72 and 39: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3.
The GCF of 72 and 39 is 3.
GCF of 72 and 39 Using Prime Factorization
To find the GCF of 72 and 39 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 72: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
Prime Factors of 39: 39 = 3 × 13
Step 2: Now, identify the common prime factors The common prime factor is: 3
Step 3: Multiply the common prime factors 3 = 3
The Greatest Common Factor of 72 and 39 is 3.
GCF of 72 and 39 Using Division Method or Euclidean Algorithm Method
Find the GCF of 72 and 39 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 39 72 ÷ 39 = 1 (quotient),
The remainder is calculated as 72 − (39×1) = 33
The remainder is 33, not zero, so continue the process
Step 2: Now divide the previous divisor (39) by the previous remainder (33)
Divide 39 by 33 39 ÷ 33 = 1 (quotient), remainder = 39 − (33×1) = 6
Step 3: Now divide the previous divisor (33) by the previous remainder (6)
Divide 33 by 6 33 ÷ 6 = 5 (quotient), remainder = 33 − (6×5) = 3
Step 4: Now divide the previous divisor (6) by the previous remainder (3)
Divide 6 by 3 6 ÷ 3 = 2 (quotient), remainder = 6 − (3×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 72 and 39 is 3.
Common Mistakes and How to Avoid Them in GCF of 72 and 39
Finding the GCF of 72 and 39 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 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 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 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 72 and 39 Examples
Problem 1
A baker has 72 cookies and 39 cupcakes. She wants to pack them into boxes with the same number of items in each box, using the largest number of items possible. How many items will be in each box?
We should find the GCF of 72 and 39 GCF of 72 and 39 3
There are 3 equal items per box. 72 ÷ 3 = 24 39 ÷ 3 = 13
There will be 3 items in each box, with 24 boxes containing cookies and 13 boxes containing cupcakes.
Explanation
As the GCF of 72 and 39 is 3, the baker can make boxes containing 3 items each.
Now divide 72 and 39 by 3.
Each box contains 3 items.
Problem 2
A gardener has 72 tulip bulbs and 39 daffodil bulbs. They want to plant them in rows with the same number of bulbs in each row, using the largest possible number of bulbs per row. How many bulbs will be in each row?
GCF of 72 and 39 3 So each row will have 3 bulbs.
Explanation
There are 72 tulip bulbs and 39 daffodil bulbs.
To find the total number of bulbs in each row, we should find the GCF of 72 and 39.
There will be 3 bulbs in each row.
Problem 3
A tailor has 72 meters of silk and 39 meters of cotton 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 39
The GCF of 72 and 39 3
The fabric is 3 meters long.
Explanation
For calculating the longest length of fabric, first we need to calculate the GCF of 72 and 39, which is 3.
The length of each piece of fabric will be 3 meters.
Problem 4
A carpenter has two wooden boards, one 72 cm long and the other 39 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 39 3
The longest length of each piece is 3 cm.
Explanation
To find the longest length of each piece of the two wooden boards, 72 cm and 39 cm, respectively, we have to find the GCF of 72 and 39, which is 3 cm.
The longest length of each piece is 3 cm.
Problem 5
If the GCF of 72 and ‘b’ is 3, and the LCM is 936. Find ‘b’.
The value of ‘b’ is 39.
Explanation
GCF x LCM = product of the numbers
3 × 936 = 72 × b
2808 = 72b
b = 2808 ÷ 72 = 39
FAQs on the Greatest Common Factor of 72 and 39
1.What is the LCM of 72 and 39?
2.Is 72 divisible by 4?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 39?
5.Are 72 and 39 prime numbers?
Important Glossaries for GCF of 72 and 39
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, 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 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 36 is 72.
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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.
