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102 LearnersLast updated on September 19, 2025
GCF of 8 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 8 and 3.
What is the GCF of 8 and 3?
The greatest common factor of 8 and 3 is 1. The largest divisor of two or more numbers is called the GCF of the numbers. 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 8 and 3?
To find the GCF of 8 and 3, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 8 and 3 by Using Listing of Factors
Steps to find the GCF of 8 and 3 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 8 = 1, 2, 4, 8.
Factors of 3 = 1, 3.
Step 2: Now, identify the common factors of them Common factor of 8 and 3: 1.
Step 3: Choose the largest factor The largest factor that both numbers have is 1. The GCF of 8 and 3 is 1.
GCF of 8 and 3 Using Prime Factorization
To find the GCF of 8 and 3 using Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 8: 8 = 2 × 2 × 2 = 2³
Prime Factors of 3: 3 = 3
Step 2: Now, identify the common prime factors There are no common prime factors other than 1.
Step 3: Multiply the common prime factors There are no common prime factors to multiply, so the GCF is 1.
The Greatest Common Factor of 8 and 3 is 1.
GCF of 8 and 3 Using Division Method or Euclidean Algorithm Method
Find the GCF of 8 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 8 by 3 8 ÷ 3 = 2 (quotient),
The remainder is calculated as 8 − (3 × 2) = 2 The remainder is 2, not zero, so continue the process
Step 2: Now divide the previous divisor (3) by the previous remainder (2)
Divide 3 by 2 3 ÷ 2 = 1 (quotient), remainder = 3 − (2 × 1) = 1
The remainder is 1, not zero, so continue the process
Step 3: 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 8 and 3 is 1.
Common Mistakes and How to Avoid Them in GCF of 8 and 3
Finding GCF of 8 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 8, 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.
Mistake 3
Forgetting to include 1 as a factor
Sometimes students may forget 1 as a common factor of the numbers. It is crucial since the GCF of co-prime numbers is 1. 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 greater than 1
Students may assume that GCF of two numbers is always greater than 1. But it's not true that GCF can be 1 especially in co-prime numbers. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 8 and 3 Examples
Problem 1
A gardener has 8 rose bushes and 3 tulip plants. She wants to group them into sets with the largest number of plants in each group. How many plants will be in each group?
We should find the GCF of 8 and 3 GCF of 8 and 3
The common factor is 1.
There is 1 plant in each group. 8 ÷ 1 = 8 3 ÷ 1 = 3
There will be 1 plant in each group.
Explanation
As the GCF of 8 and 3 is 1, the gardener can make 1 group.
Now divide 8 and 3 by 1.
Each group gets 8 rose bushes and 3 tulip plants.
Problem 2
A chef has 8 kilograms of potatoes and 3 kilograms of onions. He wants to use them in recipes with the same amount of ingredients, using the largest possible quantity for each. How much of each will be used?
GCF of 8 and 3 The common factor is 1.
So each recipe will use 1 kilogram of each ingredient.
Explanation
There are 8 kilograms of potatoes and 3 kilograms of onions.
To find the largest quantity used in each recipe, we should find the GCF of 8 and 3.
There will be 1 kilogram of each in each recipe.
Problem 3
A librarian has 8 fiction books and 3 non-fiction books. She wants to arrange them in sections with an equal number of books, using the maximum possible number of books per section. How many books will be in each section?
For calculating the maximum number of books per section, we have to calculate the GCF of 8 and 3
The GCF of 8 and 3 The common factor is 1.
Each section has 1 book.
Explanation
For calculating the maximum number of books per section, first, we need to calculate the GCF of 8 and 3, which is 1.
Each section will have 1 book.
Problem 4
A farmer has two plots of land, one of 8 acres and the other of 3 acres. He wants to divide them into the largest possible equal parts, without any land left over. How large should each part be?
The farmer needs the largest piece of land GCF of 8 and 3
The common factor is 1.
The largest length of each part is 1 acre.
Explanation
To find the largest length of each part of the two plots of land, 8 acres and 3 acres, respectively, we have to find the GCF of 8 and 3, which is 1 acre.
The largest length of each piece is 1 acre.
Problem 5
If the GCF of 8 and ‘b’ is 1, and the LCM is 24. Find ‘b’.
The value of ‘b’ is 24.
Explanation
GCF × LCM = product of the numbers
1 × 24 = 8 × b
24 = 8b
b = 24 ÷ 8 = 3
FAQs on the Greatest Common Factor of 8 and 3
1.What is the LCM of 8 and 3?
2.Is 8 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 3?
5.Are 8 and 3 prime numbers?
Important Glossaries for GCF of 8 and 3
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- Prime Factors: These are the factors of a number that are prime numbers and divide the given number completely. For example, the prime factor of 3 is 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 8 is divided by 3, the remainder is 2 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 8 and 3 is 24.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 8 and 3 is 1, as it is their largest common factor that divides the numbers completely.
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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.
