101 LearnersLast updated on August 5th, 2025
GCF of 9 and 14
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 9 and 14.
What is the GCF of 9 and 14?
The greatest common factor of 9 and 14 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 9 and 14?
To find the GCF of 9 and 14, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 9 and 14 by Using Listing of factors
Steps to find the GCF of 9 and 14 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 9 = 1, 3, 9.
Factors of 14 = 1, 2, 7, 14.
Step 2: Now, identify the common factors of them Common factors of 9 and 14: 1.
Step 3: Choose the largest factor
The largest factor that both numbers have is 1.
The GCF of 9 and 14 is 1.
GCF of 9 and 14 Using Prime Factorization
To find the GCF of 9 and 14 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 9: 9 = 3 × 3 = 3²
Prime Factors of 14: 14 = 2 × 7
Step 2: Now, identify the common prime factors
There are no common prime factors.
Step 3: Since there are no common factors, the GCF is 1.
The Greatest Common Factor of 9 and 14 is 1.
GCF of 9 and 14 Using Division Method or Euclidean Algorithm Method
Find the GCF of 9 and 14 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 14 by 9 14 ÷ 9 = 1 (quotient),
The remainder is calculated as 14 − (9×1) = 5
The remainder is 5, not zero, so continue the process
Step 2: Now divide the previous divisor (9) by the previous remainder (5)
Divide 9 by 5 9 ÷ 5 = 1 (quotient), remainder = 9 − (5×1) = 4
Step 3: Divide the previous divisor (5) by the remainder (4) 5 ÷ 4 = 1 (quotient), remainder = 5 − (4×1) = 1
Step 4: Divide the previous divisor (4) by the remainder (1) 4 ÷ 1 = 4 (quotient), remainder = 4 − (1×4) = 0
The remainder is zero, so the divisor will become the GCF.
The GCF of 9 and 14 is 1.
Common Mistakes and How to Avoid Them in GCF of 9 and 14
Finding the GCF of 9 and 14 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 14, students may mention 10, 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 a factor that is not common or the smallest common factor instead of the largest one. To avoid this confusion, students should list all the common factors and verify the greatest one.
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 here, it highlights the importance of complete understanding. Students should remember to 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 be clear on the definitions of multiples and factors.
Mistake 5
Assuming GCF is always greater than 1
Students may assume that the GCF of two numbers will always be greater than 1. But when two numbers are co-prime, their GCF is 1. To avoid this, students should focus on common factors rather than assumptions.
Greatest Common Factor of 9 and 14 Examples
Problem 1
A gardener has 9 rose bushes and 14 tulip plants. She wants to plant them in rows with the same number of plants in each row, using the largest possible number of plants per row. How many plants will be in each row?
We should find the GCF of 9 and 14 GCF of 9 and 14
The GCF is 1.
There will be 1 plant in each row.
Explanation
As the GCF of 9 and 14 is 1, the gardener can plant 1 plant per row.
Problem 2
A teacher has 9 notebooks and 14 markers. She wants to distribute them equally among students, with the largest number of items in each group. How many items will be in each group?
GCF of 9 and 14 The GCF is 1.
So each group will have 1 item.
Explanation
There are 9 notebooks and 14 markers. To find the total number of items in each group, we should find the GCF of 9 and 14. There will be 1 item in each group.
Problem 3
A cook has 9 kg of potatoes and 14 kg of carrots. She wants to make soups with equal amounts of each, using the largest possible amount. What should be the amount of each ingredient in each soup?
For calculating equal amounts, we have to calculate the GCF of 9 and 14
The GCF is 1.
Each soup will have 1 kg of each ingredient.
Explanation
For calculating the largest equal amount of ingredients, first, we need to calculate the GCF of 9 and 14, which is 1. Each soup will have 1 kg of potatoes and 1 kg of carrots.
Problem 4
A carpenter has two wooden planks, one 9 cm long and the other 14 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 9 and 14
The GCF 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, 9 cm and 14 cm, respectively, we have to find the GCF of 9 and 14, which is 1 cm. The longest length of each piece is 1 cm.
Problem 5
If the GCF of 9 and ‘a’ is 3, and the LCM is 42, find ‘a’.
The value of ‘a’ is 14.
Explanation
GCF × LCM = product of the numbers 3 × 42 = 9 × a
126 = 9a
a = 126 ÷ 9 = 14
FAQs on the Greatest Common Factor of 9 and 14
1.What is the LCM of 9 and 14?
2.Is 9 divisible by 2?
3.What will be the GCF of any two co-prime numbers?
4.What is the prime factorization of 9?
5.Are 9 and 14 prime numbers?
6.How can children in Australia use numbers in everyday life to understand GCF of 9 and 14?
7.What are some fun ways kids in Australia can practice GCF of 9 and 14 with numbers?
8.What role do numbers and GCF of 9 and 14 play in helping children in Australia develop problem-solving skills?
9.How can families in Australia create number-rich environments to improve GCF of 9 and 14 skills?
Important Glossaries for GCF of 9 and 14
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 9 are 1, 3, and 9.
- Co-prime Numbers: Two numbers are co-prime if their greatest common factor is 1. For instance, 9 and 14 are co-prime.
- 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 14 is divided by 9, the remainder is 5.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 9 and 14 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.
