102 LearnersLast updated on August 5th, 2025
GCF of 24 and 100
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 24 and 100.
What is the GCF of 24 and 100?
The greatest common factor of 24 and 100 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 24 and 100?
To find the GCF of 24 and 100, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 24 and 100 by Using Listing of factors
Steps to find the GCF of 24 and 100 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 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100.
Step 2: Now, identify the common factors of them
Common factors of 24 and 100: 1, 2, 4.
Step 3: Choose the largest factor
The largest factor that both numbers have is 4.
The GCF of 24 and 100 is 4.
GCF of 24 and 100 Using Prime Factorization
To find the GCF of 24 and 100 using 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 = 2³ x 3
Prime Factors of 100: 100 = 2 x 2 x 5 x 5 = 2² x 5²
Step 2: Now, identify the common prime factors
The common prime factor is: 2 x 2 = 2²
Step 3: Multiply the common prime factors
2² = 4
The Greatest Common Factor of 24 and 100 is 4.
GCF of 24 and 100 Using Division Method or Euclidean Algorithm Method
Find the GCF of 24 and 100 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number
Here, divide 100 by 24
100 ÷ 24 = 4 (quotient),
The remainder is calculated as 100 − (24×4) = 4
The remainder is 4, not zero, so continue the process
Step 2: Now divide the previous divisor (24) by the previous remainder (4)
Divide 24 by 4
24 ÷ 4 = 6 (quotient),
remainder = 24 − (4×6) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 24 and 100 is 4.
Common Mistakes and How to Avoid Them in GCF of 24 and 100
Finding GCF of 24 and 100 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 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 24 and 100 Examples
Problem 1
A baker has 24 cupcakes and 100 cookies. She wants to package them into boxes with the largest number of items in each box. How many items will be in each box?
We should find GCF of 24 and 100
GCF of 24 and 100 2² = 4.
There are 4 equal boxes
24 ÷ 4 = 6
100 ÷ 4 = 25
There will be 4 boxes, and each box gets 6 cupcakes and 25 cookies.
Explanation
As the GCF of 24 and 100 is 4, the baker can make 4 boxes.
Now divide 24 and 100 by 4.
Each box gets 6 cupcakes and 25 cookies.
Problem 2
A school has 24 laptops and 100 tablets. They want to arrange them in rows with the same number of devices in each row, using the largest possible number of devices per row. How many devices will be in each row?
GCF of 24 and 100 2² = 4.
So each row will have 4 devices.
Explanation
There are 24 laptops and 100 tablets.
To find the total number of devices in each row, we should find the GCF of 24 and 100.
There will be 4 devices in each row.
Problem 3
A florist has 24 roses and 100 daisies. She wants to make bouquets with an equal number of flowers, using the longest possible length. How many flowers should be in each bouquet?
For calculating the longest equal length, we have to calculate the GCF of 24 and 100
The GCF of 24 and 100 2² = 4.
Each bouquet will have 4 flowers.
Explanation
For calculating the longest length of the bouquet, first we need to calculate the GCF of 24 and 100, which is 4.
Each bouquet will have 4 flowers.
Problem 4
A painter has two canvases, one 24 inches wide and the other 100 inches wide. He wants to cut them into the longest possible equal pieces, without any canvas left over. What should be the width of each piece?
The painter needs the longest piece of canvas
GCF of 24 and 100 2² = 4.
The longest width of each piece is 4 inches.
Explanation
To find the longest width of each piece of the two canvases, 24 inches and 100 inches, respectively.
We have to find the GCF of 24 and 100, which is 4 inches.
The longest width of each piece is 4 inches.
Problem 5
If the GCF of 24 and ‘b’ is 4, and the LCM is 600. Find ‘b’.
The value of ‘b’ is 100.
Explanation
GCF × LCM = product of the numbers
4 × 600 = 24 × b
2400 = 24b
b = 2400 ÷ 24 = 100
FAQs on the Greatest Common Factor of 24 and 100
1.What is the LCM of 24 and 100?
2.Is 24 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 100?
5.Are 24 and 100 prime numbers?
6.How can children in India use numbers in everyday life to understand GCF of 24 and 100?
7.What are some fun ways kids in India can practice GCF of 24 and 100 with numbers?
8.What role do numbers and GCF of 24 and 100 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve GCF of 24 and 100 skills?
Important Glossaries for GCF of 24 and 100
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 8 are 1, 2, 4, and 8.
- 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 11 is divided by 3, the remainder is 2 and the quotient is 3.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 100 is 600.
- GCF: The largest factor that commonly divides two or more numbers. For example, the GCF of 24 and 100 will be 4, as it is their largest common factor that divides the numbers completely.
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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.
