103 LearnersLast updated on August 5th, 2025
GCF of 3 and 4
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 schedule events. In this topic, we will learn about the GCF of 3 and 4.
What is the GCF of 3 and 4?
The greatest common factor of 3 and 4 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 3 and 4?
To find the GCF of 3 and 4, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 3 and 4 by Using Listing of Factors
Steps to find the GCF of 3 and 4 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 3 = 1, 3.
Factors of 4 = 1, 2, 4.
Step 2: Now, identify the common factors of them. Common factor of 3 and 4: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 3 and 4 is 1.
GCF of 3 and 4 Using Prime Factorization
To find the GCF of 3 and 4 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 3: 3 = 3
Prime Factors of 4: 4 = 2 x 2 = 2²
Step 2: Now, identify the common prime factors 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 3 and 4 is 1.
GCF of 3 and 4 Using Division Method or Euclidean Algorithm Method
Find the GCF of 3 and 4 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 4 by 3 4 ÷ 3 = 1 (quotient),
The remainder is calculated as 4 − (3×1) = 1
The remainder is 1, not zero, so continue the process
Step 2: Now divide the previous divisor (3) by the previous remainder (1)
Divide 3 by 1 3 ÷ 1 = 3 (quotient), remainder = 3 − (1×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 3 and 4 is 1.
Common Mistakes and How to Avoid Them in GCF of 3 and 4
Finding GCF of 3 and 4 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 3, students may mention 6, 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, which in the case of 3 and 4 is 1.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. Although it does not affect the GCF, it indicates an incomplete understanding of factors. Students should always include 1 as a factor.
Mistake 4
Using Multiples instead of factors
Students may confuse 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 is always greater than 1. However, if the numbers are co-prime, their GCF is 1. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 3 and 4 Examples
Problem 1
A teacher has 3 apples and 4 oranges. She 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 the GCF of 3 and 4 GCF of 3 and 4 is 1.
There is only 1 item in each group.
3 ÷ 1 = 3
4 ÷ 1 = 4
There will be 1 item in each group.
Explanation
As the GCF of 3 and 4 is 1, the teacher can make groups with 1 item in each.
Each group will contain 1 apple or 1 orange.
Problem 2
A school has 3 red flags and 4 blue flags. They want to arrange them in rows with the same number of flags in each row, using the largest possible number of flags per row. How many flags will be in each row?
GCF of 3 and 4 is 1. So each row will have 1 flag.
Explanation
There are 3 red and 4 blue flags. To find the total number of flags in each row, we should find the GCF of 3 and 4.
There will be 1 flag in each row.
Problem 3
A tailor has 3 meters of red fabric and 4 meters of blue 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 3 and 4
The GCF of 3 and 4 is 1.
Each piece of fabric will be 1 meter long.
Explanation
For calculating the longest length of the fabric, we first need to calculate the GCF of 3 and 4, which is 1. The length of each piece of fabric will be 1 meter.
Problem 4
A carpenter has two wooden planks, one 3 cm long and the other 4 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.
GCF of 3 and 4 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, 3 cm and 4 cm, respectively, we have to find the GCF of 3 and 4, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 3 and ‘a’ is 1, and the LCM is 12. Find ‘a’.
The value of ‘a’ is 4.
Explanation
GCF x LCM = product of the numbers
1 × 12 = 3 × a
12 = 3a
a = 12 ÷ 3 = 4
FAQs on the Greatest Common Factor of 3 and 4
1.What is the LCM of 3 and 4?
2.Is 3 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 4?
5.Are 3 and 4 prime numbers?
6.How can children in Vietnam use numbers in everyday life to understand GCF of 3 and 4?
7.What are some fun ways kids in Vietnam can practice GCF of 3 and 4 with numbers?
8.What role do numbers and GCF of 3 and 4 play in helping children in Vietnam develop problem-solving skills?
9.How can families in Vietnam create number-rich environments to improve GCF of 3 and 4 skills?
Important Glossaries for GCF of 3 and 4
- Factors: Numbers that divide a target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
- Prime Factors: These are the prime numbers that multiply together to give the original number. For example, the prime factors of 18 are 2 and 3.
- Co-prime: Two numbers are co-prime if their greatest common factor is 1. For example, 8 and 15 are co-prime.
- 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.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 3 and 4 is 12.
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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.
