105 LearnersLast updated on August 5th, 2025
GCF of 10 and 20
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 10 and 20.
What is the GCF of 10 and 20?
The greatest common factor of 10 and 20 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 20?
To find the GCF of 10 and 20, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / Euclidean Algorithm
GCF of 10 and 20 by Using Listing of Factors
Steps to find the GCF of 10 and 20 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 10 = 1, 2, 5, 10.
Factors of 20 = 1, 2, 4, 5, 10, 20.
Step 2: Now, identify the common factors Common factors of 10 and 20: 1, 2, 5, 10.
Step 3: Choose the largest factor
The largest factor that both numbers have is 10.
The GCF of 10 and 20 is 10.
GCF of 10 and 20 Using Prime Factorization
To find the GCF of 10 and 20 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 10: 10 = 2 x 5
Prime Factors of 20: 20 = 2 x 2 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 10 and 20 is 10.
GCF of 10 and 20 Using Division Method or Euclidean Algorithm Method
Find the GCF of 10 and 20 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 20 by 10 20 ÷ 10 = 2 (quotient),
The remainder is calculated as 20 − (10×2) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 10 and 20 is 10.
Common Mistakes and How to Avoid Them in GCF of 10 and 20
Finding the GCF of 10 and 20 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 10, students may mention 3 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 the GCF of two numbers will always be an even number. But it's not true; 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 20 Examples
Problem 1
A chef has 10 apples and 20 oranges. He wants to create fruit baskets with the largest number of total fruits in each basket. How many fruits will be in each basket?
We should find the GCF of 10 and 20 GCF of 10 and 20 is 10.
There are 10 equal baskets 10 ÷ 10 = 1
20 ÷ 10 = 2
There will be 10 baskets, and each basket gets 1 apple and 2 oranges.
Explanation
As the GCF of 10 and 20 is 10, the chef can make 10 baskets. Now divide 10 and 20 by 10. Each basket gets 1 apple and 2 oranges.
Problem 2
A class has 10 boys and 20 girls. They want to form teams with the same number of boys and girls in each team, using the largest possible number of total students per team. How many students will be in each team?
GCF of 10 and 20 is 10.
So each team will have 10 students.
Explanation
There are 10 boys and 20 girls. To find the total number of students in each team, we should find the GCF of 10 and 20. There will be 10 students in each team.
Problem 3
A farmer has 10 meters of white fencing and 20 meters of green fencing. He wants to cut both 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 20
The GCF of 10 and 20 is 10.
The fencing is 10 meters long.
Explanation
For calculating the longest length of the fencing, first, we need to calculate the GCF of 10 and 20, which is 10. The length of each piece of the fencing will be 10 meters.
Problem 4
A painter has two canvas rolls, one 10 meters long and the other 20 meters long. He wants to cut them into the longest possible equal pieces, without any canvas left over. What should be the length of each piece?
The painter needs the longest piece of canvas GCF of 10 and 20 is 10.
The longest length of each piece is 10 meters.
Explanation
To find the longest length of each piece of the two canvas rolls, 10 meters and 20 meters, respectively, we have to find the GCF of 10 and 20, which is 10 meters. The longest length of each piece is 10 meters.
Problem 5
If the GCF of 10 and ‘b’ is 10, and the LCM is 20. Find ‘b’.
The value of ‘b’ is 20.
Explanation
GCF x LCM = product of the numbers 10 × 20 = 10 × b
200 = 10b
b = 200 ÷ 10 = 20
FAQs on the Greatest Common Factor of 10 and 20
1.What is the LCM of 10 and 20?
2.Is 10 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 20?
5.Are 10 and 20 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 10 and 20?
7.What are some fun ways kids in India can practice GCF of 10 and 20 with numbers?
8.What role do numbers and GCF of 10 and 20 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 10 and 20 skills?
Important Glossaries for GCF of 10 and 20
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- 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 20 are 2 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 10 is divided by 3, the remainder is 1 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 10 and 20 is 20.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 10 and 20 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.
