101 LearnersLast updated on August 1st, 2025
GCF of 14 and 28
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 14 and 28.
What is the GCF of 14 and 28?
The greatest common factor of 14 and 28 is 14. 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 14 and 28?
To find the GCF of 14 and 28, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 14 and 28 by Using Listing of Factors
Steps to find the GCF of 14 and 28 using the listing of factors:
Step 1: Firstly, list the factors of each number.
Factors of 14 = 1, 2, 7, 14.
Factors of 28 = 1, 2, 4, 7, 14, 28.
Step 2: Now, identify the common factors of them.
Common factors of 14 and 28: 1, 2, 7, 14.
Step 3: Choose the largest factor.
The largest factor that both numbers have is 14.
The GCF of 14 and 28 is 14.
GCF of 14 and 28 Using Prime Factorization
To find the GCF of 14 and 28 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number.
Prime Factors of 14: 14 = 2 x 7.
Prime Factors of 28: 28 = 2 x 2 x 7.
Step 2: Now, identify the common prime factors.
The common prime factors are: 2 x 7.
Step 3: Multiply the common prime factors.
2 x 7 = 14.
The Greatest Common Factor of 14 and 28 is 14.
GCF of 14 and 28 Using Division Method or Euclidean Algorithm Method
Find the GCF of 14 and 28 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 28 by 14. 28 ÷ 14 = 2 (quotient),
The remainder is calculated as 28 − (14×2) = 0.
The remainder is zero, the divisor will become the GCF.
The GCF of 14 and 28 is 14.
Common Mistakes and How to Avoid Them in GCF of 14 and 28
Finding the GCF of 14 and 28 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 5 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 shows an 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 14 and 28 Examples
Problem 1
A baker has 14 chocolate cupcakes and 28 vanilla cupcakes. She wants to pack them in boxes with the same number of cupcakes in each box, using the largest number of cupcakes possible. How many cupcakes will be in each box?
We should find the GCF of 14 and 28.
GCF of 14 and 28 is 14.
There are 14 cupcakes in each box.
Explanation
As the GCF of 14 and 28 is 14, the baker can make boxes with 14 cupcakes each. This ensures that each box has an equal number of chocolate and vanilla cupcakes.
Problem 2
A gardener has 14 red roses and 28 white roses. She wants to arrange them in bouquets with the same number of roses in each bouquet, using the largest possible number of roses per bouquet. How many roses will be in each bouquet?
GCF of 14 and 28 is 14.
So each bouquet will have 14 roses.
Explanation
There are 14 red roses and 28 white roses. To find the total number of roses in each bouquet, we should find the GCF of 14 and 28. There will be 14 roses in each bouquet.
Problem 3
A shopkeeper has 14 meters of red fabric and 28 meters of blue fabric. He 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 14 and 28.
The GCF of 14 and 28 is 14.
Each piece of fabric is 14 meters long.
Explanation
For calculating the longest length of the fabric first, we need to calculate the GCF of 14 and 28, which is 14. The length of each piece of fabric will be 14 meters.
Problem 4
A carpenter has two wooden planks, one 14 cm long and the other 28 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 14 and 28 is 14.
The longest length of each piece is 14 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 14 cm and 28 cm, respectively, we have to find the GCF of 14 and 28, which is 14 cm. The longest length of each piece is 14 cm.
Problem 5
If the GCF of 14 and ‘a’ is 2, and the LCM is 56. Find ‘a’.
The value of ‘a’ is 4.
Explanation
GCF × LCM = product of the numbers 2 × 56 = 14 × a
112 = 14a
a = 112 ÷ 14 = 8
FAQs on the Greatest Common Factor of 14 and 28
1.What is the LCM of 14 and 28?
2.Is 28 divisible by 7?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 28?
5.Are 14 and 28 prime numbers?
6.How can children in United Arab Emirates use numbers in everyday life to understand GCF of 14 and 28?
7.What are some fun ways kids in United Arab Emirates can practice GCF of 14 and 28 with numbers?
8.What role do numbers and GCF of 14 and 28 play in helping children in United Arab Emirates develop problem-solving skills?
9.How can families in United Arab Emirates create number-rich environments to improve GCF of 14 and 28 skills?
Important Glossaries for GCF of 14 and 28
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 14 are 1, 2, 7, and 14.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 7 are 7, 14, 21, 28, 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 28 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 29 is divided by 5, the remainder is 4 and the quotient is 5.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 and 28 is 28.
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.
