101 LearnersLast updated on August 5th, 2025
GCF of 10 and 30
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 10 and 30.
What is the GCF of 10 and 30?
The greatest common factor of 10 and 30 is 10. 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 10 and 30?
To find the GCF of 10 and 30, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 10 and 30 by Using Listing of factors
Steps to find the GCF of 10 and 30 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 10 = 1, 2, 5, 10.
Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30.
Step 2: Now, identify the common factors of them Common factors of 10 and 30: 1, 2, 5, 10.
Step 3: Choose the largest factor
The largest factor that both numbers have is 10.
The GCF of 10 and 30 is 10.
GCF of 10 and 30 Using Prime Factorization
To find the GCF of 10 and 30 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 10: 10 = 2 × 5
Prime Factors of 30: 30 = 2 × 3 × 5
Step 2: Now, identify the common prime factors
The common prime factors are: 2 × 5
Step 3: Multiply the common prime factors 2 × 5 = 10.
The Greatest Common Factor of 10 and 30 is 10.
GCF of 10 and 30 Using Division Method or Euclidean Algorithm Method
Find the GCF of 10 and 30 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 30 by 10 30 ÷ 10 = 3 (quotient),
The remainder is calculated as 30 − (10×3) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 10 and 30 is 10.
Common Mistakes and How to Avoid Them in GCF of 10 and 30
Finding GCF of 10 and 30 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 10, students may mention 8, 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 that 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 10 and 30 Examples
Problem 1
A chef has 10 tomatoes and 30 potatoes. 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 GCF of 10 and 30 GCF of 10 and 30 is 10.
There are 10 equal groups 10 ÷ 10 = 1
30 ÷ 10 = 3
There will be 10 groups, and each group gets 1 tomato and 3 potatoes.
Explanation
As the GCF of 10 and 30 is 10, the chef can make 10 groups. Now divide 10 and 30 by 10. Each group gets 1 tomato and 3 potatoes.
Problem 2
A concert venue has 10 spotlights and 30 speakers. They want to arrange them in rows with the same number of items in each row, using the largest possible number of items per row. How many items will be in each row?
GCF of 10 and 30 is 10.
So each row will have 10 items.
Explanation
There are 10 spotlights and 30 speakers. To find the total number of items in each row, we should find the GCF of 10 and 30. There will be 10 items in each row.
Problem 3
An artist has 10 meters of canvas and 30 meters of thread. She wants to cut both materials 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 10 and 30
The GCF of 10 and 30 is 10.
The length of each piece is 10 meters.
Explanation
For calculating the longest length of the materials, first, we need to calculate the GCF of 10 and 30, which is 10. The length of each piece will be 10 meters.
Problem 4
A landscaper has two paths, one 10 meters long and the other 30 meters long. He wants to divide them into the longest possible equal sections, without any leftover. What should be the length of each section?
The landscaper needs the longest section GCF of 10 and 30 is 10.
The longest length of each section is 10 meters.
Explanation
To find the longest length of each section of the two paths, 10 meters and 30 meters, respectively, we have to find the GCF of 10 and 30, which is 10 meters. The longest length of each section is 10 meters.
Problem 5
If the GCF of 10 and ‘a’ is 10, and the LCM is 30. Find ‘a’.
The value of ‘a’ is 30.
Explanation
GCF × LCM = product of the numbers 10 × 30 = 10 × a
300 = 10a
a = 300 ÷ 10 = 30
FAQs on the Greatest Common Factor of 10 and 30
1.What is the LCM of 10 and 30?
2.Is 10 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 30?
5.Are 10 and 30 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 10 and 30?
7.What are some fun ways kids in United States can practice GCF of 10 and 30 with numbers?
8.What role do numbers and GCF of 10 and 30 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 10 and 30 skills?
Important Glossaries for GCF of 10 and 30
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- 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 10 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 4, 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 10 and 30 is 30.
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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.
