102 LearnersLast updated on August 5th, 2025
GCF of 24 and 56
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 to schedule events. In this topic, we will learn about the GCF of 24 and 56.
What is the GCF of 24 and 56?
The greatest common factor of 24 and 56 is 8. 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 24 and 56?
To find the GCF of 24 and 56, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 24 and 56 by Using Listing of Factors
Steps to find the GCF of 24 and 56 using the listing of factors
Step 1: Firstly, list the factors of each number
Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 56 = 1, 2, 4, 7, 8, 14, 28, 56.
Step 2: Now, identify the common factors of them Common factors of 24 and 56: 1, 2, 4, 8.
Step 3: Choose the largest factor
The largest factor that both numbers have is 8.
The GCF of 24 and 56 is 8.
GCF of 24 and 56 Using Prime Factorization
To find the GCF of 24 and 56 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 24: 24 = 2 x 2 x 2 x 3 = 2^3 x 3
Prime Factors of 56: 56 = 2 x 2 x 2 x 7 = 2^3 x 7
Step 2: Now, identify the common prime factors
The common prime factor is: 2 x 2 x 2 = 2^3
Step 3: Multiply the common prime factors 2^3 = 8.
The Greatest Common Factor of 24 and 56 is 8.
GCF of 24 and 56 Using Division Method or Euclidean Algorithm Method
Find the GCF of 24 and 56 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 56 by 24 56 ÷ 24 = 2 (quotient),
The remainder is calculated as 56 − (24×2) = 8
The remainder is 8, not zero, so continue the process
Step 2: Now divide the previous divisor (24) by the previous remainder (8)
Divide 24 by 8 24 ÷ 8 = 3 (quotient), remainder = 24 − (8×3) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 24 and 56 is 8.
Common Mistakes and How to Avoid Them in GCF of 24 and 56
Finding the GCF of 24 and 56 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 24, students may mention 10, 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 24 and 56 Examples
Problem 1
A gardener has 24 rose bushes and 56 tulip plants. She wants to arrange them in equal rows with the largest number of plants in each row. How many plants will be in each row?
We should find the GCF of 24 and 56 GCF of 24 and 56 2^3 = 8.
There are 8 equal rows 24 ÷ 8 = 3 56 ÷ 8 = 7
There will be 8 plants in each row, and each row will have 3 rose bushes and 7 tulip plants.
Explanation
As the GCF of 24 and 56 is 8, the gardener can make 8 rows.
Now divide 24 and 56 by 8.
Each row gets 3 rose bushes and 7 tulip plants.
Problem 2
A chef has 24 apples and 56 oranges. He wants to create fruit baskets with the largest number of fruits in each basket while keeping the count of apples and oranges the same in each basket. How many fruits will each basket contain?
GCF of 24 and 56 2^3 = 8.
So each basket will have 8 fruits.
Explanation
There are 24 apples and 56 oranges.
To find the total number of fruits in each basket, we should find the GCF of 24 and 56.
There will be 8 fruits in each basket.
Problem 3
A painter has 24 liters of red paint and 56 liters of blue paint. He wants to mix them into buckets with equal quantities of both colors, using the maximum possible amount in each bucket. What should be the volume of each bucket?
For calculating the maximum equal volume, we have to calculate the GCF of 24 and 56
The GCF of 24 and 56 2^3 = 8.
The bucket will have 8 liters of paint.
Explanation
To calculate the maximum volume of paint in the bucket, we first need to calculate the GCF of 24 and 56, which is 8.
The volume of each bucket will be 8 liters.
Problem 4
A seamstress has a 24-meter roll of silk fabric and a 56-meter roll of cotton fabric. 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 seamstress needs the longest piece of fabric GCF of 24 and 56 2^3 = 8.
The longest length of each piece is 8 meters.
Explanation
To find the longest length of each piece of the two rolls of fabric, 24 meters and 56 meters respectively, we have to find the GCF of 24 and 56, which is 8 meters.
The longest length of each piece is 8 meters.
Problem 5
If the GCF of 24 and ‘a’ is 8, and the LCM is 168, find ‘a’.
The value of ‘a’ is 56.
Explanation
GCF x LCM = product of the numbers 8 × 168 = 24 × a
1344 = 24a
a = 1344 ÷ 24 = 56
FAQs on the Greatest Common Factor of 24 and 56
1.What is the LCM of 24 and 56?
2.Is 56 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 56?
5.Are 24 and 56 prime numbers?
6.How can children in United States use numbers in everyday life to understand GCF of 24 and 56?
7.What are some fun ways kids in United States can practice GCF of 24 and 56 with numbers?
8.What role do numbers and GCF of 24 and 56 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 24 and 56 skills?
Important Glossaries for GCF of 24 and 56
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 8 are 8, 16, 24, 32, 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 56 are 2 and 7.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 56 is divided by 8, the remainder is 0 and the quotient is 7.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 56 is 168.
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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.
