102 LearnersLast updated on August 11th, 2025
GCF of 14 and 21
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 21.
What is the GCF of 14 and 21?
The greatest common factor of 14 and 21 is 7. 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 21?
To find the GCF of 14 and 21, a few methods are described below - Listing Factors Prime Factorization Long Division Method / by Euclidean Algorithm
GCF of 14 and 21 by Using Listing of Factors
Steps to find the GCF of 14 and 21 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 14 = 1, 2, 7, 14.
Factors of 21 = 1, 3, 7, 21.
Step 2: Now, identify the common factors of them Common factors of 14 and 21: 1, 7.
Step 3: Choose the largest factor The largest factor that both numbers have is 7. The GCF of 14 and 21 is 7.
GCF of 14 and 21 Using Prime Factorization
To find the GCF of 14 and 21 using 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 21: 21 = 3 x 7
Step 2: Now, identify the common prime factors The common prime factor is: 7
Step 3: Multiply the common prime factors The Greatest Common Factor of 14 and 21 is 7.
GCF of 14 and 21 Using Division Method or Euclidean Algorithm Method
Find the GCF of 14 and 21 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 21 by 14 21 ÷ 14 = 1 (quotient), The remainder is calculated as 21 − (14×1) = 7 The remainder is 7, not zero, so continue the process
Step 2: Now divide the previous divisor (14) by the previous remainder (7) Divide 14 by 7 14 ÷ 7 = 2 (quotient), remainder = 14 − (7×2) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 14 and 21 is 7.
Common Mistakes and How to Avoid Them in GCF of 14 and 21
Finding GCF of 14 and 21 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 tells about the incomplete understanding of the factors. 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 an even number
Students may assume that GCF of two numbers will always be an even number. But it's not true that 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 21 Examples
Problem 1
A gardener has 14 red roses and 21 white roses. He wants to arrange them in bouquets with the same number of roses in each bouquet, using the most roses possible. How many roses will each bouquet have?
We should find GCF of 14 and 21 GCF of 14 and 21 7 There are 7 roses in each bouquet.
Explanation
As the GCF of 14 and 21 is 7, the gardener can make bouquets with 7 roses each.
Problem 2
A coach has 14 soccer balls and 21 basketballs. He wants to distribute them into equal groups, with the largest number of balls in each group. How many balls will be in each group?
GCF of 14 and 21 7 So each group will have 7 balls.
Explanation
There are 14 soccer balls and 21 basketballs. To find the total number of balls in each group, we should find the GCF of 14 and 21. There will be 7 balls in each group.
Problem 3
A chef has 14 oranges and 21 apples. He wants to create fruit baskets with the same number of fruits in each basket, using the most fruits possible. How many fruits should be in each basket?
For calculating the longest equal length, we have to calculate the GCF of 14 and 21 The GCF of 14 and 21 7 Each basket will have 7 fruits.
Explanation
For calculating the number of fruits in each basket first, we need to calculate the GCF of 14 and 21, which is 7. Thus, each basket will have 7 fruits.
Problem 4
A tailor has two pieces of fabric, one 14 meters long and the other 21 meters long. She wants to cut them into the longest possible equal pieces, without any fabric left over. What should be the length of each piece?
The tailor needs the longest piece of fabric GCF of 14 and 21 7 The longest length of each piece is 7 meters.
Explanation
To find the longest length of each piece of the two fabric pieces, 14 meters and 21 meters, respectively. We have to find the GCF of 14 and 21, which is 7 meters. The longest length of each piece is 7 meters.
Problem 5
If the GCF of 14 and ‘b’ is 7, and the LCM is 42. Find ‘b’.
The value of ‘b’ is 21.
Explanation
GCF x LCM = product of the numbers 7 × 42 = 14 × b 294 = 14b b = 294 ÷ 14 = 21
FAQs on the Greatest Common Factor of 14 and 21
1.What is the LCM of 14 and 21?
2.Is 14 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 21?
5.Are 14 and 21 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 14 and 21?
7.What are some fun ways kids in United States can practice GCF of 14 and 21 with numbers?
8.What role do numbers and GCF of 14 and 21 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 14 and 21 skills?
Important Glossaries for GCF of 14 and 21
- 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 3 are 3, 6, 9, 12, 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 21 are 3 and 7.
- 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 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 14 and 21 is 42.
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.
