106 LearnersLast updated on August 5th, 2025
GCF of 330 and 180
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 to schedule events. In this topic, we will learn about the GCF of 330 and 180.
What is the GCF of 330 and 180?
The greatest common factor of 330 and 180 is 30. The largest divisor of two or more numbers is called the GCF of the numbers. 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 330 and 180?
To find the GCF of 330 and 180, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 330 and 180 by Using Listing of Factors
Steps to find the GCF of 330 and 180 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 330 = 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330.
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 330 and 180: 1, 2, 3, 5, 6, 10, 15, 30.
Step 3: Choose the largest factor
The largest factor that both numbers have is 30.
The GCF of 330 and 180 is 30.
GCF of 330 and 180 Using Prime Factorization
To find the GCF of 330 and 180 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 330: 330 = 2 × 3 × 5 × 11
Prime Factors of 180: 180 = 2 × 2 × 3 × 3 × 5
Step 2: Now, identify the common prime factors
The common prime factors are: 2 × 3 × 5
Step 3: Multiply the common prime factors
2 × 3 × 5 = 30.
The Greatest Common Factor of 330 and 180 is 30.
GCF of 330 and 180 Using Division Method or Euclidean Algorithm Method
Find the GCF of 330 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 330 by 180
330 ÷ 180 = 1 (quotient), The remainder is calculated as 330 − (180×1) = 150
The remainder is 150, not zero, so continue the process
Step 2: Now divide the previous divisor (180) by the previous remainder (150)
Divide 180 by 150
180 ÷ 150 = 1 (quotient), remainder = 180 − (150×1) = 30
Step 3: Divide the previous divisor (150) by the previous remainder (30)
150 ÷ 30 = 5 (quotient), remainder = 150 − (30×5) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 330 and 180 is 30.
Common Mistakes and How to Avoid Them in GCF of 330 and 180
Finding the GCF of 330 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 330, students may mention 25 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 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 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 330 and 180 Examples
Problem 1
A gardener has 330 tulip bulbs and 180 daffodil bulbs. She wants to plant them in rows with the largest number of bulbs in each row. How many bulbs will be in each row?
We should find the GCF of 330 and 180
GCF of 330 and 180
2 × 3 × 5 = 30.
There are 30 bulbs in each row.
330 ÷ 30 = 11
180 ÷ 30 = 6
There will be 30 bulbs in each row, with 11 rows of tulips and 6 rows of daffodils.
Explanation
As the GCF of 330 and 180 is 30, the gardener can make rows with 30 bulbs each.
Now divide 330 and 180 by 30.
There are 11 rows of tulip bulbs and 6 rows of daffodil bulbs.
Problem 2
A concert hall has 330 seats in the orchestra section and 180 seats in the balcony. They want to arrange them in blocks with the same number of seats in each block, using the largest possible number of seats per block. How many seats will be in each block?
GCF of 330 and 180
2 × 3 × 5 = 30
So each block will have 30 seats.
Explanation
There are 330 seats in the orchestra section and 180 in the balcony.
To find the total number of seats in each block, we should find the GCF of 330 and 180.
There will be 30 seats in each block.
Problem 3
A painter has 330 meters of blue paint tape and 180 meters of red paint tape. He wants to cut both tapes 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 330 and 180.
The GCF of 330 and 180
2 × 3 × 5 = 30
The length of each piece is 30 meters.
Explanation
For calculating the longest length of the paint tape, first, we need to calculate the GCF of 330 and 180, which is 30.
The length of each piece of tape will be 30 meters.
Problem 4
A carpenter has two wooden planks, one 330 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 330 and 180 2 × 3 × 5 = 30.
The longest length of each piece is 30 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 330 cm and 180 cm, respectively, we have to find the GCF of 330 and 180, which is 30 cm.
The longest length of each piece is 30 cm.
Problem 5
If the GCF of 330 and ‘b’ is 30, and the LCM is 1980, find ‘b’.
The value of ‘b’ is 180.
Explanation
GCF × LCM = product of the numbers
30 × 1980 = 330 × b
59400 = 330b
b = 59400 ÷ 330 = 180
FAQs on the Greatest Common Factor of 330 and 180
1.What is the LCM of 330 and 180?
2.Is 180 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 330?
5.Are 330 and 180 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 330 and 180?
7.What are some fun ways kids in India can practice GCF of 330 and 180 with numbers?
8.What role do numbers and GCF of 330 and 180 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 330 and 180 skills?
Important Glossaries for GCF of 330 and 180
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 6 are 6, 12, 18, 24, 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 330 are 2, 3, 5, and 11.
- 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 330 and 180 is 1980.
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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.
