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102 LearnersLast updated on September 19, 2025
GCF of 2 and 10
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 2 and 10.
What is the GCF of 2 and 10?
The greatest common factor of 2 and 10 is 2. 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 2 and 10?
To find the GCF of 2 and 10, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 2 and 10 by Using Listing of Factors
Steps to find the GCF of 2 and 10 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 2 = 1, 2.
Factors of 10 = 1, 2, 5, 10.
Step 2: Now, identify the common factors of them Common factors of 2 and 10: 1, 2.
Step 3: Choose the largest factor The largest factor that both numbers have is 2.
The GCF of 2 and 10 is 2.
GCF of 2 and 10 Using Prime Factorization
To find the GCF of 2 and 10 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 2: 2 = 2
Prime Factors of 10: 10 = 2 x 5
Step 2: Now, identify the common prime factors The common prime factor is: 2
Step 3: Multiply the common prime factors 2 = 2
The Greatest Common Factor of 2 and 10 is 2.
GCF of 2 and 10 Using Division Method or Euclidean Algorithm Method
Find the GCF of 2 and 10 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 10 by 2 10 ÷ 2 = 5 (quotient),
The remainder is calculated as 10 - (2x5) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 2 and 10 is 2.
Common Mistakes and How to Avoid Them in GCF of 2 and 10
Finding the GCF of 2 and 10 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 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 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 2 and 10 Examples
Problem 1
A gardener has 2 apple trees and 10 orange trees. She wants to plant them in rows with an equal number of trees in each row using the largest number of trees per row. How many trees will be in each row?
We should find the GCF of 2 and 10 GCF of 2 and 10 2
So, each row will have 2 trees.
Explanation
As the GCF of 2 and 10 is 2, the gardener can plant the trees in rows with 2 trees in each row.
Problem 2
A baker has 2 loaves of bread and 10 pastries. They want to arrange them in boxes with the same number of items in each box, using the largest possible number of items per box. How many items will be in each box?
GCF of 2 and 10 2
So, each box will have 2 items.
Explanation
There are 2 loaves of bread and 10 pastries.
To find the total number of items in each box, we should find the GCF of 2 and 10.
Each box will have 2 items.
Problem 3
A runner has 2 red flags and 10 blue flags. She wants to divide them into sets of equal size, using the largest possible number of flags per set. How many flags will be in each set?
For calculating the largest equal size, we have to calculate the GCF of 2 and 10
The GCF of 2 and 10 2
Each set will have 2 flags.
Explanation
For calculating the largest size of the sets, we first need to calculate the GCF of 2 and 10, which is 2.
Each set will have 2 flags.
Problem 4
A decorator has two ribbons, one 2 meters long and the other 10 meters long. He wants to cut them into the longest possible equal pieces, without any ribbon left over. What should be the length of each piece?
The decorator needs the longest piece of ribbon GCF of 2 and 10 2
The longest length of each piece is 2 meters.
Explanation
To find the longest length of each piece of the two ribbons, 2 meters and 10 meters, respectively, we have to find the GCF of 2 and 10, which is 2 meters.
The longest length of each piece is 2 meters.
Problem 5
If the GCF of 2 and ‘b’ is 2, and the LCM is 10, find ‘b’.
The value of ‘b’ is 10.
Explanation
GCF x LCM = product of the numbers
2 x 10 = 2 x b
20 = 2b
b = 20 ÷ 2 = 10
FAQs on the Greatest Common Factor of 2 and 10
1.What is the LCM of 2 and 10?
2.Is 2 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 10?
5.Are 2 and 10 prime numbers?
Important Glossaries for GCF of 2 and 10
- 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 2 are 2, 4, 6, 8, 10, 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 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 2 and 10 is 10.
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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.
