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100 LearnersLast updated on September 9, 2025
GCF of 24 and 84
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 84.
What is the GCF of 24 and 84?
The greatest common factor of 24 and 84 is 12. 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 84?
To find the GCF of 24 and 84, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 24 and 84 by Using Listing of Factors
Steps to find the GCF of 24 and 84 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 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
Step 2: Now, identify the common factors of them Common factors of 24 and 84: 1, 2, 3, 4, 6, 12.
Step 3: Choose the largest factor The largest factor that both numbers have is 12. The GCF of 24 and 84 is 12.
GCF of 24 and 84 Using Prime Factorization
To find the GCF of 24 and 84 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number Prime Factors of 24: 24 = 2 × 2 × 2 × 3 = 2³ × 3 Prime Factors of 84: 84 = 2 × 2 × 3 × 7 = 2² × 3 × 7
Step 2: Now, identify the common prime factors The common prime factors are: 2 × 2 × 3 = 2² × 3
Step 3: Multiply the common prime factors 2² × 3 = 4 × 3 = 12.
The Greatest Common Factor of 24 and 84 is 12.
GCF of 24 and 84 Using Division Method or Euclidean Algorithm Method
Find the GCF of 24 and 84 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number Here, divide 84 by 24 84 ÷ 24 = 3 (quotient), The remainder is calculated as 84 − (24 × 3) = 12 The remainder is 12, not zero, so continue the process
Step 2: 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 84 is 12.
Common Mistakes and How to Avoid Them in GCF of 24 and 84
Finding GCF of 24 and 84 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 84 Examples
Problem 1
A gardener has 24 pots of red flowers and 84 pots of blue flowers. She wants to arrange them into groups with the largest number of pots in each group. How many pots will be in each group?
We should find the GCF of 24 and 84 GCF of 24 and 84 2² × 3 = 4 × 3 = 12. There are 12 equal groups 24 ÷ 12 = 2 84 ÷ 12 = 7 There will be 12 groups, and each group gets 2 pots of red flowers and 7 pots of blue flowers.
Explanation
As the GCF of 24 and 84 is 12, the gardener can make 12 groups.
Now divide 24 and 84 by 12.
Each group gets 2 pots of red flowers and 7 pots of blue flowers.
Problem 2
A decorator has 24 meters of red fabric and 84 meters of blue fabric. She wants to cut both fabrics into pieces of equal length, using the longest possible length. What should be the length of each piece?
For calculating the longest equal length, we have to calculate the GCF of 24 and 84 The GCF of 24 and 84 2² × 3 = 4 × 3 = 12. The fabric is 12 meters long.
Explanation
For calculating the longest length of the fabric, first we need to calculate the GCF of 24 and 84 which is 12.
The length of each piece of fabric will be 12 meters.
Problem 3
A chef has 24 pieces of chicken and 84 pieces of beef for a barbecue. He wants to create equal servings with the largest number of pieces in each serving. How many pieces will be in each serving?
GCF of 24 and 84 2² × 3 = 4 × 3 = 12. Each serving will have 12 pieces.
Explanation
To find how many pieces will be in each serving, calculate the GCF of 24 and 84, which is 12.
Each serving will include 12 pieces.
Problem 4
A teacher has 24 books on one topic and 84 books on another topic. She wants to organize them into the largest possible identical groups. How many books will be in each group?
The teacher needs the largest group of books GCF of 24 and 84 2² × 3 = 4 × 3 = 12.
Each group will have 12 books.
Explanation
To find the largest identical groups of books, we find the GCF of 24 and 84, which is 12.
There will be 12 books in each group.
Problem 5
If the GCF of 24 and ‘b’ is 12, and the LCM is 168. Find ‘b’.
The value of ‘b’ is 84.
Explanation
GCF x LCM = product of the numbers
12 × 168
= 24 × b
2016 = 24b
b = 2016 ÷ 24 = 84
FAQs on the Greatest Common Factor of 24 and 84
1.What is the LCM of 24 and 84?
2.Is 84 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 84?
5.Are 24 and 84 prime numbers?
Important Glossaries for GCF of 24 and 84
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 4 are 4, 8, 12, 16, 20, 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 15 are 3 and 5.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 12 is divided by 7, the remainder is 5 and the quotient is 1.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 24 and 84 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.
