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103 LearnersLast updated on September 24, 2025
GCF of 192 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 schedule events. In this topic, we will learn about the GCF of 192 and 72.
What is the GCF of 192 and 72?
The greatest common factor of 192 and 72 is 24. 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 192 and 72?
To find the GCF of 192 and 72, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 192 and 72 by Using Listing of Factors
Steps to find the GCF of 192 and 72 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 192 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192.
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 192 and 72: 1, 2, 3, 4, 6, 8, 12, 24.
Step 3: Choose the largest factor The largest factor that both numbers have is 24.
The GCF of 192 and 72 is 24.
GCF of 192 and 72 Using Prime Factorization
To find the GCF of 192 and 72 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime factors of 192: 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3 = 26 x 3
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 2 x 3 = 23 x 3
Step 3: Multiply the common prime factors 23 x 3 = 8 × 3 = 24.
The Greatest Common Factor of 192 and 72 is 24.
GCF of 192 and 72 Using Division Method or Euclidean Algorithm Method
Find the GCF of 192 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 192 by 72 192 ÷ 72 = 2 (quotient), The remainder is calculated as 192 − (72×2) = 48
The remainder is 48, not zero, so continue the process
Step 2: Now divide the previous divisor (72) by the previous remainder (48) Divide 72 by 48 72 ÷ 48 = 1 (quotient), remainder = 72 − (48×1) = 24
The remainder is 24, not zero, so continue the process
Step 3: Now divide the previous divisor (48) by the previous remainder (24) Divide 48 by 24 48 ÷ 24 = 2 (quotient), remainder = 48 − (24×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 192 and 72 is 24.
Common Mistakes and How to Avoid Them in GCF of 192 and 72
Finding the GCF of 192 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 192, 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 192 and 72 Examples
Problem 1
A landscaper has 192 tulips and 72 daffodils. She wants to plant them in equal groups, with the largest number of flowers in each group. How many flowers will be in each group?
We should find the GCF of 192 and 72 GCF of 192 and 72 23 x 3 = 8 x 3 = 24.
There are 24 equal groups 192 ÷ 24 = 8 72 ÷ 24 = 3
There will be 24 groups, and each group gets 8 tulips and 3 daffodils.
Explanation
As the GCF of 192 and 72 is 24, the landscaper can make 24 groups. Now divide 192 and 72 by 24. Each group gets 8 tulips and 3 daffodils.
Problem 2
A factory has 192 red widgets and 72 blue widgets. They want to pack them in boxes with the same number of widgets in each box, using the largest possible number of widgets per box. How many widgets will be in each box?
GCF of 192 and 72 23 x 3 = 8 × 3 = 24.
So each box will have 24 widgets.
Explanation
There are 192 red and 72 blue widgets.
To find the total number of widgets in each box, we should find the GCF of 192 and 72.
There will be 24 widgets in each box.
Problem 3
A tailor has 192 meters of silk fabric and 72 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 192 and 72
The GCF of 192 and 72 23 x 3 = 8 × 3 = 24.
The fabric is 24 meters long.
Explanation
For calculating the longest length of the fabric first we need to calculate the GCF of 192 and 72 which is 24.
The length of each piece of the fabric will be 24 meters.
Problem 4
A carpenter has two wooden planks, one 192 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 192 and 72 23 x 3 = 8 × 3 = 24.
The longest length of each piece is 24 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 192 cm and 72 cm, respectively. We have to find the GCF of 192 and 72, which is 24 cm.
The longest length of each piece is 24 cm.
Problem 5
If the GCF of 192 and ‘a’ is 24, and the LCM is 576. Find ‘a’.
The value of ‘a’ is 72.
Explanation
GCF x LCM = product of the numbers
24 × 576 = 192 × a
13824 = 192a
a = 13824 ÷ 192 = 72
FAQs on the Greatest Common Factor of 192 and 72
1.What is the LCM of 192 and 72?
2.Is 192 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 72?
5.Are 192 and 72 prime numbers?
Important Glossaries for GCF of 192 and 72
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
- 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 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 15 is divided by 4, the remainder is 3 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 12 is 24.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 100 and 80 will be 20, 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.
