103 LearnersLast updated on August 11th, 2025
GCF of 20 and 24
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 20 and 24.
What is the GCF of 20 and 24?
The greatest common factor of 20 and 24 is 4. 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 20 and 24?
To find the GCF of 20 and 24, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 20 and 24 by Using Listing of factors
Steps to find the GCF of 20 and 24 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 20 = 1, 2, 4, 5, 10, 20.
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Step 2: Now, identify the common factors of them Common factors of 20 and 24: 1, 2, 4.
Step 3: Choose the largest factor The largest factor that both numbers have is 4. The GCF of 20 and 24 is 4.
GCF of 20 and 24 Using Prime Factorization
To find the GCF of 20 and 24 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 20: 20 = 2 x 2 x 5 = 22 x 5
Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 23 x 3
Step 2: Now, identify the common prime factors The common prime factors are: 2 x 2 = 22
Step 3: Multiply the common prime factors 22 = 4.
The Greatest Common Factor of 20 and 24 is 4.
GCF of 20 and 24 Using Division Method or Euclidean Algorithm Method
Find the GCF of 20 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 20 24 ÷ 20 = 1 (quotient), The remainder is calculated as 24 − (20×1) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (20) by the previous remainder (4) Divide 20 by 4 20 ÷ 4 = 5 (quotient), remainder = 20 − (4×5) = 0
The remainder is zero, the divisor will become the GCF. The GCF of 20 and 24 is 4.
Common Mistakes and How to Avoid Them in GCF of 20 and 24
Finding GCF of 20 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 20, students may mention 7 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 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 20 and 24 Examples
Problem 1
A gardener has 20 roses and 24 tulips. She wants to create bouquets with the largest number of flowers in each bouquet. How many flowers will be in each bouquet?
We should find the GCF of 20 and 24 GCF of 20 and 24 22 = 4.
There are 4 equal bouquets 20 ÷ 4 = 5 24 ÷ 4 = 6
There will be 4 bouquets, and each bouquet gets 5 roses and 6 tulips.
Explanation
As the GCF of 20 and 24 is 4, the gardener can make 4 bouquets. Now divide 20 and 24 by 4. Each bouquet gets 5 roses and 6 tulips.
Problem 2
A chef has 20 red apples and 24 green apples. She wants to arrange them in baskets with the same number of apples in each basket, using the largest possible number of apples per basket. How many apples will be in each basket?
GCF of 20 and 24 2^2 = 4. So each basket will have 4 apples.
Explanation
There are 20 red apples and 24 green apples. To find the total number of apples in each basket, we should find the GCF of 20 and 24. There will be 4 apples in each basket.
Problem 3
An artist has 20 meters of red yarn and 24 meters of blue yarn. She wants to cut both yarns 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 20 and 24 The GCF of 20 and 24 2^2 = 4. The yarn is 4 meters long.
Explanation
For calculating the longest length of the yarn first, we need to calculate the GCF of 20 and 24, which is 4. The length of each piece of yarn will be 4 meters.
Problem 4
A carpenter has two wooden planks, one 20 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 20 and 24 2^2 = 4. The longest length of each piece is 4 cm.
Explanation
To find the longest length of each piece of the two wooden planks, 20 cm and 24 cm respectively, we have to find the GCF of 20 and 24, which is 4 cm. The longest length of each piece is 4 cm.
Problem 5
If the GCF of 20 and ‘a’ is 4, and the LCM is 120. Find ‘a’.
The value of ‘a’ is 24.
Explanation
GCF x LCM = product of the numbers 4 × 120 = 20 × a 480 = 20a a = 480 ÷ 20 = 24
FAQs on the Greatest Common Factor of 20 and 24
1.What is the LCM of 20 and 24?
2.Is 20 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 20?
5.Are 20 and 24 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 20 and 24?
7.What are some fun ways kids in India can practice GCF of 20 and 24 with numbers?
8.What role do numbers and GCF of 20 and 24 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 20 and 24 skills?
Important Glossaries for GCF of 20 and 24
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 10 are 1, 2, 5, and 10.
- 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 18 are 2 and 3.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 13 is divided by 5, the remainder is 3 and the quotient is 2.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 20 and 24 is 120.
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.
