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126 LearnersLast updated on December 11, 2025
GCF of 12 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 12 and 72.
What is the GCF of 12 and 72?
The greatest common factor of 12 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 12 and 72?
To find the GCF of 12 and 72, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 12 and 72 by Using Listing of factors
Steps to find the GCF of 12 and 72 using the listing of factors
Step 1: Firstly, list the factors of each number Factors of 12 = 1, 2, 3, 4, 6, 12. 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 12 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 12 and 72 is 12.
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GCF of 12 and 72 Using Prime Factorization
To find the GCF of 12 and 72 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 12: 12 = 2 × 2 × 3 = 2² × 3 Prime Factors of 72: 72 = 2 × 2 × 2 × 3 × 3 = 2³ × 3²
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 × 3 = 2² × 3
Step 3: Multiply the common prime factors 2² × 3 = 4 × 3 = 12. The Greatest Common Factor of 12 and 72 is 12.
GCF of 12 and 72 Using Division Method or Euclidean Algorithm Method
Find the GCF of 12 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 12 72 ÷ 12 = 6 (quotient), remainder = 72 - (12 × 6) = 0 The remainder is zero, so the divisor will become the GCF.
The GCF of 12 and 72 is 12.
Common Mistakes and How to Avoid Them in GCF of 12 and 72
Finding the GCF of 12 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 12, 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 12 and 72 Examples
Problem 1
A gardener has 12 roses and 72 tulips. She wants to create flower arrangements with the largest possible number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 12 and 72
GCF of 12 and 72 = 2² × 3 = 4 × 3 = 12.
There are 12 flowers in each bouquet.
12 ÷ 12 = 1
72 ÷ 12 = 6
There will be 12 bouquets, and each bouquet gets 1 rose and 6 tulips.
Explanation
As the GCF of 12 and 72 is 12, the gardener can make 12 bouquets.
Now divide 12 and 72 by 12.
Each bouquet gets 1 rose and 6 tulips.
Problem 2
A chef has 12 small cakes and 72 cookies. He wants to arrange them on trays with the largest possible number of each item per tray. How many items will be on each tray?
GCF of 12 and 72
2² × 3 = 4 × 3 = 12.
So each tray will have 12 items.
Explanation
There are 12 small cakes and 72 cookies.
To find the total number of items on each tray, we should find the GCF of 12 and 72.
There will be 12 items on each tray.
Problem 3
A teacher has 12 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 12 and 72
The GCF of 12 and 72
2² × 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 12 and 72, which is 12.
The length of each piece of fabric will be 12 meters.
Problem 4
A carpenter has two wooden planks, one 12 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 12 and 72
2² × 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, 12 cm and 72 cm, respectively.
We have to find the GCF of 12 and 72, which is 12 cm.
The longest length of each piece is 12 cm.
Problem 5
If the GCF of 12 and โbโ is 12, and the LCM is 144. Find โbโ.
The value of ‘b’ is 72.
Explanation
GCF × LCM = product of the numbers
12 × 144 = 12 × b
1728= 12b
b= 1728 ÷ 12 = 144
FAQs on the Greatest Common Factor of 12 and 72
1.What is the LCM of 12 and 72?
2.Is 12 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 72?
5.Are 12 and 72 prime numbers?
Important Glossaries for GCF of 12 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.
- 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, 15, 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 12 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 5, the remainder is 2 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 12 and 72 is 72.
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.
