Summarize this article:
101 LearnersLast updated on September 9, 2025
GCF of 2 and 3
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 3.
What is the GCF of 2 and 3?
The greatest common factor of 2 and 3 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 3?
To find the GCF of 2 and 3, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 2 and 3 by Using Listing of Factors
Steps to find the GCF of 2 and 3 using the listing of factors:
Step 1: Firstly, list the factors of each number Factors of 2 = 1, 2. Factors of 3 = 1, 3.
Step 2: Now, identify the common factors of them Common factor of 2 and 3: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 2 and 3 is 1.
GCF of 2 and 3 Using Prime Factorization
To find the GCF of 2 and 3 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 3: 3 = 3
Step 2: Now, identify the common prime factors There are no common prime factors.
Step 3: As there are no common prime factors, the GCF is 1. The Greatest Common Factor of 2 and 3 is 1.
GCF of 2 and 3 Using Division Method or Euclidean Algorithm Method
Find the GCF of 2 and 3 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 3 by 2 3 ÷ 2 = 1 (quotient), The remainder is calculated as 3 − (2×1) = 1 The remainder is 1, 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 3 is 1.
Common Mistakes and How to Avoid Them in GCF of 2 and 3
Finding GCF of 2 and 3 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 2, students may mention 4, 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.
However, in this case, since there is only one common factor, this step is straightforward.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers.
Although it is the only common factor for co-prime numbers like 2 and 3, students should include 1 to ensure complete understanding of the factors.
Mistake 4
Using Multiples instead of factors
Students confuse factors with 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 2 and 3 Examples
Problem 1
A gardener has 2 apple trees and 3 pear trees. He wants to plant them in rows with an equal number of trees in each row. What is the largest number of trees he can have in each row?
We should find the GCF of 2 and 3. The GCF of 2 and 3 is 1. There will be 1 tree in each row.
Explanation
As the GCF of 2 and 3 is 1, the gardener can only plant 1 tree per row for both apple and pear trees.
Problem 2
A baker has 2 loaves of bread and 3 cakes. He wants to arrange them into trays with the same number of items on each tray. What is the largest number of items he can place on each tray?
The GCF of 2 and 3 is 1. So each tray will have 1 item.
Explanation
There are 2 loaves of bread and 3 cakes.
To find the total number of items on each tray, we should find the GCF of 2 and 3.
There will be 1 item on each tray.
Problem 3
A tailor has 2 meters of silk fabric and 3 meters of cotton fabric. She wants to cut both fabrics 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 2 and 3. The GCF of 2 and 3 is 1. The length of each piece is 1 meter.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 2 and 3, which is 1.
The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 2 cm long and the other 3 cm long. He wants to cut them into the longest possible equal pieces, without any wood left over. What should be the length of each piece?
The carpenter needs the longest piece of wood. The GCF of 2 and 3 is 1. The longest length of each piece is 1 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 2 cm and 3 cm, respectively, we have to find the GCF of 2 and 3, which is 1 cm.
The longest length of each piece is 1 cm.
Problem 5
If the GCF of 2 and ‘a’ is 1, and the LCM is 6, find ‘a’.
The value of ‘a’ is 3.
Explanation
GCF x LCM = product of the numbers
1 × 6
= 2 × a 6
= 2a a
= 6 ÷ 2 = 3
FAQs on the Greatest Common Factor of 2 and 3
1.What is the LCM of 2 and 3?
2.Is 2 a prime number?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 3?
5.Are 2 and 3 co-prime numbers?
Important Glossaries for GCF of 2 and 3
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 2 are 1 and 2.
- Co-prime: Two numbers are co-prime if their GCF is 1, meaning they have no common factors other than 1.
- 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 3 are 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 3 is divided by 2, the remainder is 1.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 2 and 3 is 1, as it is their largest common factor that divides the numbers completely.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 2 and 3
![Important Math Links Icon]()
Next to GCF of 2 and 3
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.
