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102 LearnersLast updated on September 19, 2025
GCF of 2 and 5
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 2 and 5.
What is the GCF of 2 and 5?
The greatest common factor of 2 and 5 is 1. 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 5?
To find the GCF of 2 and 5, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 2 and 5 by Using Listing of factors
Steps to find the GCF of 2 and 5 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 2 = 1, 2.
Factors of 5 = 1, 5.
Step 2: Now, identify the common factors of them Common factor of 2 and 5: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1.
The GCF of 2 and 5 is 1.
GCF of 2 and 5 Using Prime Factorization
To find the GCF of 2 and 5 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 5: 5 = 5
Step 2: Now, identify the common prime factors The common prime factor is: 1 (as there are no common prime factors)
Step 3: Multiply the common prime factors Since there are no common prime factors, the GCF is 1.
The Greatest Common Factor of 2 and 5 is 1.
GCF of 2 and 5 Using Division Method or Euclidean Algorithm Method
Find the GCF of 2 and 5 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 5 by 2 5 ÷ 2 = 2 (quotient),
The remainder is calculated as 5 − (2×2) = 1 The remainder is not zero, so continue the process
Step 2: Now divide the previous divisor (2) by the previous remainder (1)
Divide 2 by 1 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 2 and 5 is 1.
Common Mistakes and How to Avoid Them in GCF of 2 and 5
Finding GCF of 2 and 5 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 5, students may mention 10 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 a number as a common factor when there isn't one other than 1. To avoid this confusion, students should list all the common factors and find the greatest one, which in this case is 1.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. While it is the only common factor in this case, students should include 1 as a factor to understand the complete set of factors.
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 greater than 1
Students may assume that the GCF of two numbers always has to be greater than 1. But it's not true, as the GCF can be 1, especially for co-prime numbers like 2 and 5. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 2 and 5 Examples
Problem 1
A chef has 2 apples and 5 bananas. She wants to create fruit baskets with the same number of fruits in each basket. What is the largest number of fruits that can be in each basket?
We should find the GCF of 2 and 5 GCF of 2 and 5 is 1.
There will be 1 fruit in each basket.
Explanation
As the GCF of 2 and 5 is 1, the chef can only make baskets with 1 fruit each.
Problem 2
A gardener has 2 rose bushes and 5 sunflower plants. She wants to plant them in rows with the same number of plants in each row. What is the largest number of plants that can be in each row?
GCF of 2 and 5 is 1.
So each row will have 1 plant.
Explanation
The gardener can only plant 1 plant per row since the GCF of 2 and 5 is 1.
Problem 3
A teacher has 2 markers and 5 chalks. She wants to distribute them among students equally. What is the largest number of students that can receive an equal number of markers and chalks?
For equal distribution, we have to calculate the GCF of 2 and 5
The GCF of 2 and 5 is 1.
The largest number of students is 1.
Explanation
For equal distribution, the GCF of 2 and 5 is 1, so only 1 student can receive both a marker and a chalk.
Problem 4
A tailor has 2 meters of red ribbon and 5 meters of blue ribbon. She wants to cut them into the longest possible pieces of equal length without any ribbon left over. What should be the length of each piece?
The tailor needs the longest piece of ribbon GCF of 2 and 5 is 1.
The longest length of each piece is 1 meter.
Explanation
To find the longest length of each piece of the two ribbons, 2 meters and 5 meters, respectively, we find the GCF of 2 and 5, which is 1 meter.
The longest length of each piece is 1 meter.
Problem 5
If the GCF of 2 and ‘b’ is 1, and the LCM is 10. Find ‘b’.
The value of ‘b’ is 5.
Explanation
GCF x LCM = product of the numbers
1 × 10 = 2 × b
10 = 2b
b = 10 ÷ 2 = 5
FAQs on the Greatest Common Factor of 2 and 5
1.What is the LCM of 2 and 5?
2.Is 2 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 5?
5.Are 2 and 5 prime numbers?
Important Glossaries for GCF of 2 and 5
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 5 are 1 and 5.
- Prime Numbers: Numbers greater than 1 having no divisors other than 1 and itself. For example, 2 and 5 are prime numbers.
- Greatest Common Factor (GCF): The largest factor that commonly divides two or more numbers. For example, the GCF of 2 and 5 is 1.
- Co-prime: Two numbers are co-prime if their GCF is 1. For example, 2 and 5 are co-prime.
- Least Common Multiple (LCM): The smallest common multiple of two or more numbers. For example, the LCM of 2 and 5 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.
