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124 LearnersLast updated on January 21st, 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
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?
Explanation
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?
Explanation
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?
Explanation
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?
Explanation
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 ?
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.
