107 LearnersLast updated on August 12, 2025
GCF of 21 and 24
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 to schedule events. In this topic, we will learn about the GCF of 21 and 24.
What is the GCF of 21 and 24?
The greatest common factor of 21 and 24 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 21 and 24?
To find the GCF of 21 and 24, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 21 and 24 by Using Listing of factors
Steps to find the GCF of 21 and 24 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 21 = 1, 3, 7, 21.
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Step 2: Now, identify the common factors of them Common factors of 21 and 24: 1, 3.
Step 3: Choose the largest factor The largest factor that both numbers have is 3. The GCF of 21 and 24 is 3.
GCF of 21 and 24 Using Prime Factorization
To find the GCF of 21 and 24 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 21: 21 = 3 x 7
Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 2^3 x 3
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 21 and 24 is 3.
GCF of 21 and 24 Using Division Method or Euclidean Algorithm Method
Find the GCF of 21 and 24 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 24 by 21 24 ÷ 21 = 1 (quotient), The remainder is calculated as 24 − (21×1) = 3 The remainder is 3, not zero, so continue the process
Step 2: Now divide the previous divisor (21) by the previous remainder (3) Divide 21 by 3 21 ÷ 3 = 7 (quotient), remainder = 21 − (3×7) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 21 and 24 is 3.
Common Mistakes and How to Avoid Them in GCF of 21 and 24
Finding the GCF of 21 and 24 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 21, 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 indicates an 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 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 21 and 24 Examples
Problem 1
A gardener has 21 roses and 24 tulips. She wants to arrange them in bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 21 and 24 GCF of 21 and 24 3 = 3.
There are 3 flowers in each bouquet. 21 ÷ 3 = 7 24 ÷ 3 = 8
There will be 3 bouquets, and each bouquet gets 7 roses and 8 tulips.
Explanation
As the GCF of 21 and 24 is 3, the gardener can make 3 bouquets. Now divide 21 and 24 by 3. Each bouquet gets 7 roses and 8 tulips.
Problem 2
A baker has 21 chocolate cupcakes and 24 vanilla cupcakes. She wants to arrange them in trays with the same number of cupcakes in each tray, using the largest possible number of cupcakes per tray. How many cupcakes will be in each tray?
GCF of 21 and 24 3 = 3. So each tray will have 3 cupcakes.
Explanation
There are 21 chocolate and 24 vanilla cupcakes. To find the total number of cupcakes in each tray, we should find the GCF of 21 and 24. There will be 3 cupcakes in each tray.
Problem 3
A tailor has 21 meters of red fabric and 24 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 21 and 24 The GCF of 21 and 24 3 = 3. Each piece is 3 meters long.
Explanation
For calculating the longest length of the fabric, first, we need to calculate the GCF of 21 and 24, which is 3. The length of each piece of fabric will be 3 meters.
Problem 4
A carpenter has two wooden planks, one 21 cm long and the other 24 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 21 and 24 3 = 3. The longest length of each piece is 3 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 21 cm and 24 cm, respectively. We have to find the GCF of 21 and 24, which is 3 cm. The longest length of each piece is 3 cm.
Problem 5
If the GCF of 21 and ‘a’ is 3, and the LCM is 168. Find ‘a’.
The value of ‘a’ is 24.
Explanation
GCF x LCM = product of the numbers
3 × 168 = 21 × a
504 = 21a
a = 504 ÷ 21 = 24
FAQs on the Greatest Common Factor of 21 and 24
1.What is the LCM of 21 and 24?
2.Is 21 divisible by 3?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 24?
5.Are 21 and 24 prime numbers?
6.How can children in Philippines use numbers in everyday life to understand GCF of 21 and 24?
7.What are some fun ways kids in Philippines can practice GCF of 21 and 24 with numbers?
8.What role do numbers and GCF of 21 and 24 play in helping children in Philippines develop problem-solving skills?
9.How can families in Philippines create number-rich environments to improve GCF of 21 and 24 skills?
Important Glossaries for GCF of 21 and 24
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 6 are 1, 2, 3, and 6.
- 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 factors of 21 are 3 and 7.
- 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 21 and 24 is 168.
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.
