100 LearnersLast updated on August 5th, 2025
GCF of 3 and 9
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 3 and 9.
What is the GCF of 3 and 9?
The greatest common factor of 3 and 9 is 3. 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 9?
To find the GCF of 3 and 9, a few methods are described below
- Listing Factors Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 3 and 9 by Using Listing of Factors
Steps to find the GCF of 3 and 9 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 3 = 1, 3.
Factors of 9 = 1, 3, 9.
Step 2: Now, identify the common factors of them Common factors of 3 and 9: 1, 3.
Step 3: Choose the largest factor
The largest factor that both numbers have is 3.
The GCF of 3 and 9 is 3.
GCF of 3 and 9 Using Prime Factorization
To find the GCF of 3 and 9 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 3: 3 = 3
Prime Factors of 9: 9 = 3 x 3 = 3^2
Step 2: Now, identify the common prime factors
The common prime factor is: 3
Step 3: Multiply the common prime factors 3 = 3.
The Greatest Common Factor of 3 and 9 is 3.
GCF of 3 and 9 Using Division Method or Euclidean Algorithm Method
Find the GCF of 3 and 9 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 9 by 3
9 ÷ 3 = 3 (quotient),
The remainder is calculated as 9 − (3×3) = 0
The remainder is zero, so the divisor becomes the GCF.
The GCF of 3 and 9 is 3.
Common Mistakes and How to Avoid Them in GCF of 3 and 9
Finding the GCF of 3 and 9 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided by students.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors. For example, while listing factors of 9, 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. However, it does not affect the GCF, but it tells about the 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 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 3 and 9 Examples
Problem 1
A teacher has 3 apples and 9 bananas. 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 9 GCF of 3 and 9 3
There are 3 equal groups 3 ÷ 3 = 1 9 ÷ 3 = 3
There will be 3 groups, and each group gets 1 apple and 3 bananas.
Explanation
As the GCF of 3 and 9 is 3, the teacher can make 3 groups.
Now divide 3 and 9 by 3.
Each group gets 1 apple and 3 bananas.
Problem 2
A school has 3 red balls and 9 blue balls. They want to arrange them in rows with the same number of balls in each row, using the largest possible number of balls per row. How many balls will be in each row?
GCF of 3 and 9 3 So each row will have 3 balls.
Explanation
There are 3 red balls and 9 blue balls.
To find the total number of balls in each row, we should find the GCF of 3 and 9.
There will be 3 balls in each row.
Problem 3
A tailor has 3 meters of red fabric and 9 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 9
The GCF of 3 and 9 3
The fabric is 3 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 3 and 9, which is 3.
The length of each piece of fabric will be 3 meters.
Problem 4
A carpenter has two wooden planks, one 3 cm long and the other 9 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 9 3
The longest length of each piece is 3 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 3 cm and 9 cm, respectively, we have to find the GCF of 3 and 9, which is 3 cm.
The longest length of each piece is 3 cm.
Problem 5
If the GCF of 3 and ‘b’ is 3, and the LCM is 9, find ‘b’.
The value of ‘b’ is 9.
Explanation
GCF x LCM = product of the numbers 3 × 9 = 3 × b
27 = 3b
b = 27 ÷ 3 = 9
FAQs on the Greatest Common Factor of 3 and 9
1.What is the LCM of 3 and 9?
2.Is 3 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 9?
5.Are 3 and 9 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 3 and 9?
7.What are some fun ways kids in United States can practice GCF of 3 and 9 with numbers?
8.What role do numbers and GCF of 3 and 9 play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve GCF of 3 and 9 skills?
Important Glossaries for GCF of 3 and 9
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- 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, 15, 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 factor of 9 is 3.
- 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, and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 3 and 9 is 9.
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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.
