102 LearnersLast updated on August 5th, 2025
GCF of 30 and 50
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, group or arrange items, and schedule events. In this topic, we will learn about the GCF of 30 and 50.
What is the GCF of 30 and 50?
The greatest common factor of 30 and 50 is 10. 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 30 and 50?
To find the GCF of 30 and 50, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 30 and 50 by Using Listing of Factors
Steps to find the GCF of 30 and 50 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 50 = 1, 2, 5, 10, 25, 50.
Step 2: Now, identify the common factors. Common factors of 30 and 50: 1, 2, 5, 10.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 10.
The GCF of 30 and 50 is 10.
GCF of 30 and 50 Using Prime Factorization
To find the GCF of 30 and 50 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime factors of 30: 30 = 2 x 3 x 5
Prime factors of 50: 50 = 2 x 5 x 5
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 x 5
Step 3: Multiply the common prime factors. 2 x 5 = 10.
The Greatest Common Factor of 30 and 50 is 10.
GCF of 30 and 50 Using Division Method or Euclidean Algorithm Method
Find the GCF of 30 and 50 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number. Here, divide 50 by 30. 50 ÷ 30 = 1 (quotient),
The remainder is calculated as 50 − (30×1) = 20.
The remainder is 20, not zero, so continue the process.
Step 2: Now divide the previous divisor (30) by the previous remainder (20).
Divide 30 by 20. 30 ÷ 20 = 1 (quotient), remainder = 30 − (20×1) = 10.
Step 3: Continue with the process. Now divide the previous divisor (20) by the previous remainder (10). 20 ÷ 10 = 2 (quotient), remainder = 20 − (10×2) = 0.
The remainder is zero, so the divisor becomes the GCF.
The GCF of 30 and 50 is 10.
Common Mistakes and How to Avoid Them in GCF of 30 and 50
Finding the GCF of 30 and 50 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 30, students may mention 9, 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 indicates incomplete understanding of 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 as 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 30 and 50 Examples
Problem 1
A farmer has 30 apples and 50 oranges. He wants to pack them into boxes with the largest number of fruits in each box, without mixing apples and oranges. How many fruits will be in each box?
We should find the GCF of 30 and 50.
GCF of 30 and 50 = 10.
There are 10 fruits in each box.
30 ÷ 10 = 3
50 ÷ 10 = 5
There will be 10 boxes, with 3 apples and 5 oranges in each box.
Explanation
As the GCF of 30 and 50 is 10, the farmer can pack 10 fruits in each box.
Now, divide 30 and 50 by 10.
Each box will have 3 apples and 5 oranges.
Problem 2
A concert hall has 30 speakers and 50 spotlights. They want to arrange them in rows with the same number of items in each row, using the maximum number of items per row. How many items will be in each row?
GCF of 30 and 50 = 10. So each row will have 10 items.
Explanation
There are 30 speakers and 50 spotlights. To find the total number of items in each row, we should find the GCF of 30 and 50. There will be 10 items in each row.
Problem 3
A chef has 30 kg of flour and 50 kg of sugar. He wants to divide both into equal packages, using the largest possible weight. What should be the weight of each package?
For calculating the largest equal weight, we have to calculate the GCF of 30 and 50.
The GCF of 30 and 50 = 10.
Each package will weigh 10 kg.
Explanation
For calculating the largest weight of the packages, first, we need to calculate the GCF of 30 and 50, which is 10. The weight of each package of flour or sugar will be 10 kg.
Problem 4
A carpenter has two wooden boards, one 30 cm wide and the other 50 cm wide. He wants to cut them into the widest possible equal strips, without any wood left over. What should be the width of each strip?
The carpenter needs the widest strip of wood.
GCF of 30 and 50 = 10.
The widest width of each strip is 10 cm.
Explanation
To find the widest width of each strip of the two wooden boards, 30 cm and 50 cm, respectively, we have to find the GCF of 30 and 50, which is 10 cm. The widest width of each strip is 10 cm.
Problem 5
If the GCF of 30 and ‘b’ is 10, and the LCM is 150, find ‘b’.
The value of ‘b’ is 50.
Explanation
GCF x LCM = product of the numbers
10 × 150 = 30 × b
1500 = 30b
b = 1500 ÷ 30 = 50
FAQs on the Greatest Common Factor of 30 and 50
1.What is the LCM of 30 and 50?
2.Is 30 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 50?
5.Are 30 and 50 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 30 and 50?
7.What are some fun ways kids in United States can practice GCF of 30 and 50 with numbers?
8.What role do numbers and GCF of 30 and 50 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 30 and 50 skills?
Important Glossaries for GCF of 30 and 50
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- Prime Factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 30 is 2 x 3 x 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 50 is divided by 20, the remainder is 10.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 30 and 50 is 150.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 30 and 50 is 10, 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.
