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103 LearnersLast updated on September 20, 2025
GCF of 300 and 180
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 300 and 180.
What is the GCF of 300 and 180?
The greatest common factor of 300 and 180 is 60. 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 300 and 180?
To find the GCF of 300 and 180, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 300 and 180 by Using Listing of Factors
Steps to find the GCF of 300 and 180 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 300 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300.
Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
Step 2: Now, identify the common factors of them Common factors of 300 and 180: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Step 3: Choose the largest factor The largest factor that both numbers have is 60.
The GCF of 300 and 180 is 60.
GCF of 300 and 180 Using Prime Factorization
To find the GCF of 300 and 180 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 300: 300 = 2 x 2 x 3 x 5 x 5 = 2² x 3 x 5²
Prime Factors of 180: 180 = 2 x 2 x 3 x 3 x 5 = 2² x 3² x 5
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 x 3 x 5 = 2² x 3 x 5
Step 3: Multiply the common prime factors 2² x 3 x 5 = 4 x 3 x 5 = 60.
The Greatest Common Factor of 300 and 180 is 60.
GCF of 300 and 180 Using Division Method or Euclidean Algorithm Method
Find the GCF of 300 and 180 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 300 by 180 300 ÷ 180 = 1 (quotient),
The remainder is calculated as 300 − (180×1) = 120
The remainder is 120, not zero, so continue the process
Step 2: Now divide the previous divisor (180) by the previous remainder (120)
Divide 180 by 120 180 ÷ 120 = 1 (quotient), remainder = 180 − (120×1) = 60
The remainder is 60, not zero, so continue the process
Step 3: Now divide the previous divisor (120) by the previous remainder (60)
Divide 120 by 60 120 ÷ 60 = 2 (quotient), remainder = 120 − (60×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 300 and 180 is 60.
Common Mistakes and How to Avoid Them in GCF of 300 and 180
Finding the GCF of 300 and 180 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 300, students may mention 35, 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 between 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 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 300 and 180 Examples
Problem 1
A farmer has 300 apples and 180 oranges. He 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 300 and 180 GCF of 300 and 180 2² x 3 x 5 = 4 x 3 x 5 = 60.
There are 60 equal groups 300 ÷ 60 = 5 180 ÷ 60 = 3
There will be 60 groups, and each group gets 5 apples and 3 oranges.
Explanation
As the GCF of 300 and 180 is 60, the farmer can make 60 groups.
Now divide 300 and 180 by 60.
Each group gets 5 apples and 3 oranges.
Problem 2
A factory has 300 red widgets and 180 blue widgets. They want to arrange them in rows with the same number of widgets in each row, using the largest possible number of widgets per row. How many widgets will be in each row?
GCF of 300 and 180 2² x 3 x 5 = 4 x 3 x 5 = 60.
So each row will have 60 widgets.
Explanation
There are 300 red and 180 blue widgets.
To find the total number of widgets in each row, we should find the GCF of 300 and 180.
There will be 60 widgets in each row.
Problem 3
A tailor has 300 meters of red fabric and 180 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 300 and 180.
The GCF of 300 and 180 2² x 3 x 5 = 4 x 3 x 5 = 60.
The fabric pieces are 60 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 300 and 180, which is 60.
The length of each piece of fabric will be 60 meters.
Problem 4
A carpenter has two wooden planks, one 300 cm long and the other 180 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 300 and 180
2² x 3 x 5 = 4 x 3 x 5 = 60.
The longest length of each piece is 60 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 300 cm and 180 cm, respectively, we have to find the GCF of 300 and 180, which is 60 cm.
The longest length of each piece is 60 cm.
Problem 5
If the GCF of 300 and ‘a’ is 60, and the LCM is 900, find ‘a’.
The value of ‘a’ is 180.
Explanation
GCF x LCM = product of the numbers
60 × 900 = 300 × a
54000 = 300a
a = 54000 ÷ 300 = 180
FAQs on the Greatest Common Factor of 300 and 180
1.What is the LCM of 300 and 180?
2.Is 300 divisible by 5?
3.What will be the GCF of any two consecutive numbers?
4.What is the prime factorization of 180?
5.Are 300 and 180 prime numbers?
Important Glossaries for GCF of 300 and 180
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
- 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 180 are 2, 3, and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 25 is divided by 7, the remainder is 4, and the quotient is 3.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, and so on.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 300 and 180 is 60, 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.
