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103 LearnersLast updated on September 24, 2025
GCF of 4, 6, and 3
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 4, 6, and 3.
What is the GCF of 4, 6, and 3?
The greatest common factor of 4, 6, and 3 is 1. The largest divisor of two or more numbers is called the GCF of the numbers. If numbers are co-prime, they have no common factors other than 1, so their GCF is 1.
The GCF of numbers cannot be negative because divisors are always positive.
How to find the GCF of 4, 6, and 3?
To find the GCF of 4, 6, and 3, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 4, 6, and 3 by Using Listing of Factors
Steps to find the GCF of 4, 6, and 3 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 4 = 1, 2, 4.
Factors of 6 = 1, 2, 3, 6.
Factors of 3 = 1, 3.
Step 2: Now, identify the common factors of them Common factor of 4, 6, and 3: 1.
Step 3: Choose the largest factor The largest factor that all the numbers have is 1.
The GCF of 4, 6, and 3 is 1.
GCF of 4, 6, and 3 Using Prime Factorization
To find the GCF of 4, 6, and 3 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 4: 4 = 2 x 2 = 2²
Prime Factors of 6: 6 = 2 x 3
Prime Factors of 3: 3 = 3
Step 2: Now, identify the common prime factors The common prime factor is: None, as there is no common prime factor other than 1.
Step 3: Since there's no common prime factor other than 1, the GCF is 1.
The Greatest Common Factor of 4, 6, and 3 is 1.
GCF of 4, 6, and 3 Using Division Method or Euclidean Algorithm Method
Find the GCF of 4, 6, and 3 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, choose any two numbers, such as 4 and 6.
Divide the larger number by the smaller number 6 ÷ 4 = 1 (quotient), remainder = 6 − (4×1) = 2
Step 2: Now divide the previous divisor (4) by the previous remainder (2) 4 ÷ 2 = 2 (quotient), remainder = 4 − (2×2) = 0
The remainder is zero, so the GCF of 4 and 6 is 2.
Step 3: Compare the GCF of 4 and 6 with the next number (3).
Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 − (2×1) = 1
Step 4: Divide the previous divisor (2) by the remainder (1) 2 ÷ 1 = 2 (quotient), remainder = 2 − (1×2) = 0
The remainder is zero, so the GCF of 4, 6, and 3 is 1.
Common Mistakes and How to Avoid Them in GCF of 4, 6, and 3
Finding the GCF of 4, 6, 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 4, 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, which is 1 in this case.
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 demonstrates incomplete understanding of the factors. Students should include 1 as a factor.
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 greater than 1
Students may assume that the GCF of two numbers is always greater than 1. But it's not true; a GCF can be 1 if the numbers are co-prime. To avoid this, students should focus on the actual common factors rather than assumptions.
Greatest Common Factor of 4, 6, and 3 Examples
Problem 1
A chef has 4 apples, 6 bananas, and 3 oranges. She wants to create fruit baskets with the same number of each fruit in each basket. How many fruit baskets can she make?
We should find the GCF of 4, 6, and 3. GCF of 4, 6, and 3 is 1.
There will be 1 basket, and each basket will have 4 apples, 6 bananas, and 3 oranges.
Explanation
As the GCF of 4, 6, and 3 is 1, the chef can make 1 basket.
Each basket will contain all the fruits she has.
Problem 2
A gardener has 4 rose bushes, 6 tulip plants, and 3 daffodil plants. She wants to plant them in rows with the same number of each type of plant per row. How many rows can she create?
GCF of 4, 6, and 3 is 1.
So she can create 1 row.
Explanation
To find the total number of rows, we should find the GCF of 4, 6, and 3.
There will be 1 row, with each row containing all the plants she has.
Problem 3
A jeweler has 4 gold chains, 6 silver necklaces, and 3 platinum rings. He wants to display them in equal-sized sets. What should be the number of sets?
To calculate the number of equal-sized sets, we have to calculate the GCF of 4, 6, and 3.
The GCF of 4, 6, and 3 is 1.
There will be 1 set.
Explanation
For calculating the number of equal-sized sets, first we need to calculate the GCF of 4, 6, and 3, which is 1.
The jeweler will have 1 set, with all the items displayed together.
Problem 4
A painter has 4 buckets of red paint, 6 buckets of blue paint, and 3 buckets of yellow paint. He wants to distribute them into groups with the same number of each color. How many groups can he make?
The painter needs to know the number of groups.
GCF of 4, 6, and 3 is 1.
He can make 1 group.
Explanation
To find the number of groups he can make, we have to find the GCF of 4, 6, and 3, which is 1.
He can make 1 group containing all the buckets.
Problem 5
If the GCF of 4 and 'b' is 1, and the LCM is 12, find 'b'.
The value of 'b' is 12.
Explanation
GCF x LCM = product of the numbers
1 × 12 = 4 × b
12 = 4b
b = 12 ÷ 4 = 3
FAQs on the Greatest Common Factor of 4, 6, and 3
1.What is the LCM of 4, 6, and 3?
2.Is 4 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 6?
5.Are 4, 6, and 3 prime numbers?
Important Glossaries for GCF of 4, 6, and 3
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 3 are 3, 6, 9, 12, 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 4 are 2.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 5 is divided by 2, the remainder is 1 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 4, 6, and 3 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.
