101 LearnersLast updated on August 5th, 2025
GCF of 5 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 5 and 14.
What is the GCF of 5 and 14?
The greatest common factor of 5 and 14 is 1. When 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 5 and 14?
To find the GCF of 5 and 14, a few methods are described below:
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 5 and 14 by Using Listing of Factors
Steps to find the GCF of 5 and 14 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 5 = 1, 5.
Factors of 14 = 1, 2, 7, 14.
Step 2: Now, identify the common factors.
Common factors of 5 and 14: 1.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 1.
The GCF of 5 and 14 is 1.
GCF of 5 and 14 Using Prime Factorization
To find the GCF of 5 and 14 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 5: 5 = 5
Prime Factors of 14: 14 = 2 x 7
Step 2: Now, identify the common prime factors. There are no common prime factors.
Step 3: Since there are no common prime factors, the GCF is 1.
GCF of 5 and 14 Using Division Method or Euclidean Algorithm Method
Find the GCF of 5 and 14 using the division method or Euclidean Algorithm:
Step 1: First, divide the larger number by the smaller number.
Here, divide 14 by 5. 14 ÷ 5 = 2 (quotient), remainder = 14 − (5×2) = 4.
Step 2: Now divide the previous divisor (5) by the previous remainder (4). 5 ÷ 4 = 1 (quotient), remainder = 5 − (4×1) = 1.
Step 3: Now divide the previous divisor (4) by the previous remainder (1). 4 ÷ 1 = 4 (quotient), remainder = 0.
Since the remainder is zero, the divisor will become the GCF.
The GCF of 5 and 14 is 1.
Common Mistakes and How to Avoid Them in GCF of 5 and 14
Finding the GCF of 5 and 14 looks simple, but students often make mistakes while calculating the GCF. Here are some common mistakes to be avoided.
Mistake 1
Listing Incorrect Factors
Students may sometimes list incorrect factors.
For example, while listing factors of 14, 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 an incorrect common factor. To avoid 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. While it does not affect the GCF, it indicates incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students sometimes confuse factors with multiples. In that confusion, they may write multiples instead of factors. To avoid this confusion, students should clearly understand the definitions of multiples and factors.
Mistake 5
Assuming GCF is Always Greater than 1
Students may assume that the GCF of two numbers is always greater than 1. However, when two numbers are co-prime, their GCF is 1. To avoid this, students should focus on finding common factors.
Greatest Common Factor of 5 and 14 Examples
Problem 1
A gardener has 5 rose bushes and 14 sunflower plants. She wants to create rows with the same number of plants without mixing types. What is the maximum number of plants in each row?
We should find the GCF of 5 and 14.
The GCF of 5 and 14 is 1.
Each row will have 1 plant, with separate rows for roses and sunflowers.
Explanation
As the GCF of 5 and 14 is 1, the gardener can make rows where each row has only 1 plant of the same type, ensuring separate rows for roses and sunflowers.
Problem 2
A baker has 5 loaves of bread and 14 pies. She wants to pack them in boxes with the same number of items, without mixing them. What is the maximum number of items in each box?
The GCF of 5 and 14 is 1. Each box will have 1 item, with separate boxes for bread and pies.
Explanation
There are 5 loaves of bread and 14 pies.
To find the number of items in each box, we should find the GCF of 5 and 14, which is 1.
Each box will have 1 item, ensuring separate boxes for bread and pies.
Problem 3
A coach has 5 soccer balls and 14 basketballs. He wants to arrange them in lines with the same number of balls, without mixing types. What is the maximum number of balls in each line?
For arranging balls in lines, we have to calculate the GCF of 5 and 14.
The GCF of 5 and 14 is 1.
Each line will have 1 ball of the same type.
Explanation
For arranging the maximum number of balls in lines, we need to calculate the GCF of 5 and 14, which is 1.
Each line will have 1 ball, ensuring separate lines for soccer balls and basketballs.
Problem 4
A festival organizer has 5 banners and 14 flags. He wants to display them in separate rows with the same number of items. What is the maximum number of items in each row?
The organizer needs equal rows.
The GCF of 5 and 14 is 1.
Each row will have 1 item, with separate rows for banners and flags.
Explanation
To find the maximum number of items in each row, we find the GCF of 5 and 14, which is 1. Each row will have 1 item, ensuring separate rows for banners and flags.
Problem 5
If the GCF of 5 and ‘b’ is 1, and the LCM is 70, find ‘b’.
The value of ‘b’ is 14.
Explanation
GCF × LCM = product of the numbers
1 × 70 = 5 × b
70 = 5b
b = 70 ÷ 5 = 14
FAQs on the Greatest Common Factor of 5 and 14
1.What is the LCM of 5 and 14?
2.Is 5 a prime number?
3.What will be the GCF of any two consecutive numbers?
4.What is the prime factorization of 14?
5.Are 5 and 14 prime numbers?
6.How can children in United Kingdom use numbers in everyday life to understand GCF of 5 and 14?
7.What are some fun ways kids in United Kingdom can practice GCF of 5 and 14 with numbers?
8.What role do numbers and GCF of 5 and 14 play in helping children in United Kingdom develop problem-solving skills?
9.How can families in United Kingdom create number-rich environments to improve GCF of 5 and 14 skills?
Important Glossaries for GCF of 5 and 14
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.
- Prime Numbers: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 5 is a prime number.
- Co-prime: Two numbers are co-prime if their GCF is 1. For example, 5 and 14 are co-prime.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 14 is divided by 5, the remainder is 4.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 5 and 14 is 70.
Explore More numbers
![Important Math Links Icon]()
Previous to GCF of 5 and 14
![Important Math Links Icon]()
Next to GCF of 5 and 14
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.
