Last updated on August 5th, 2025
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.
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.
To find the GCF of 24 and 56, a few methods are described below
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If the GCF of 24 and ‘a’ is 8, and the LCM is 168, find ‘a’.
The value of ‘a’ is 56.
GCF x LCM = product of the numbers 8 × 168 = 24 × a
1344 = 24a
a = 1344 ÷ 24 = 56
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.
: She loves to read number jokes and games.