201 LearnersLast updated on May 26th, 2025
GCF of 24 and 36
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 36.
What is the GCF of 24 and 36
The greatest common factor of 24 and 36 is 12. 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, which is always positive.
How to find the GCF of 24 and 36
To find the GCF of 24 and 36, a few methods are described below -
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 24 and 36 by Using Listing of factors
Steps to find GCF of 24 and 36 using the listing of factors
Step1: Firstly, list the factors of each number
Factors of 24 = 1, 2, 3, 4, 6, 12, 24.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36.9
Step2: Now, identify the common factors of them
Common factors of 24 and 36: 1, 2, 3, 4, 6, 12.
Step3: Choose the largest factor
The largest factor that both numbers have is 12.
The GCF of 24 and 36 is 12.
GCF of 24 and 36 Using Prime Factorization
To find the GCF of 24 and 36 using Prime Factorization Method, follow these steps:
Step1: Find the prime Factors of each number
Prime Factors of 24 :
24 = 2 x 2 x 2 x 3 = 23x 3
Prime Factors of 36 :
36 = 2 x 2 x 3 x 3 = 22x 32
Step2: Now, identify the common prime factors
The common prime factors are :
2 x 2 x 3 = 22x 3
Step3: Multiply the common prime factors
22x 3 = 4 × 3 = 12.
The Greatest Common Factor of 24 and 36 is 12.
GCF of 24 and 36 Using Division Method
Find the GCF of 24 and 36 using the division method, follow these steps:
Step1: First divide the larger number by the smaller number
Here, divide 36 by 24
36 ÷ 24 = 1 (quotient),
The remainder is calculated as 36 − (24×1) = 12
The remainder is 12, not zero, so continue the process
Step2: Now divide the previous divisor (24) by the previous remainder (12)
Divide 24 by 12
24 ÷ 12 = 2 (quotient), remainder = 24 − (12×2) = 0
The remainder is zero, the divisor will become the GCF.
The GCF of 24 and 36 is 12.
Common Mistakes and How to Avoid them in GCF of 24 and 36
Finding GCF of 24 and 36 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.
Highest Common Factor of 24 and 36 Examples
Problem 1
A teacher has 24 pencils and 36 erasers. She wants to group them into equal sets, with the largest number of items in each group. How many items will be in each group?
We should find GCF of 24 and 36
GCF of 24 and 36
22x 3 = 4 x 3 = 12.
There are 12 equal groups
24 ÷ 12 = 2
36 ÷ 12 = 3
There will be 12 groups and each group gets 2 pencils and 3 erasers.
Explanation
As the GCF of 24 and 36 is 12, teacher can make 12 groups. Now divide 24 and 36 with 12. Each group get 2 pencils and 3 erasers.
Problem 2
A school has 24 red chairs and 36 blue chairs. They want to arrange them in rows with the same number of chairs in each row, using the largest possible number of chairs per row. How many chairs will be in each row?
GCF of 24 and 36
22x 3 = 4 × 3 = 12.
So each row will have 12 chairs.
Explanation
There are 24 red and 36 blue chairs. To find the total number of chairs in each row, we should find the GCF of 24 and 36. There will be 12 chairs in each row.
Problem 3
A tailor has 24 meters of red ribbon and 36 meters of blue ribbon. She wants to cut both ribbons into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating longest equal length, we have to calculate the GCF of 24 and 36
The GCF of 24 and 36
22x 3 = 4 × 3 = 12.
The ribbon is 12 meters long.
Explanation
For calculating the longest length of the ribbon first we need to calculate the GCF of 24 and 36 which is 12. The length of each piece of the ribbon will be 12 meters.
Problem 4
A carpenter has two wooden planks, one 24 cm long and the other 36 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 24 and 36
22x 3 = 4 × 3 = 12.
The longest length of each piece is 12 cm.
Explanation
To find the longest length of each piece of two wooden planks, 24 cm and 36 cm respectively. We have to find the GCF of 24 and 36 which is 12 cm. The longest length of each piece is 12 cm.
FAQs on Greatest Common Factor of 24 and 26
1.What is the LCM of 24 and 36?
2.Is 24 divisible by 2?
3.What is the prime factorization of 36?
4.Are 24 and 36 prime numbers?
5.What is the GCF of 24 and 42 ?
6.How can children in Oman use numbers in everyday life to understand GCF of 24 and 36?
7.What are some fun ways kids in Oman can practice GCF of 24 and 36 with numbers?
8.What role do numbers and GCF of 24 and 36 play in helping children in Oman develop problem-solving skills?
9.How can families in Oman create number-rich environments to improve GCF of 24 and 36 skills?
Important Glossaries for GCF of 24 and 36
- Multiples: A multiple of a number is the product of that number and a whole number.Example: 24 is a multiple of 6.
- Prime Numbers: It is a number that has exactly two divisors, which are 1 and itself.For example: 2 is a prime number.
- Co-prime numbers: Co-Primes are two or more numbers which do not have any other common factor except 1.
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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.
