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101 LearnersLast updated on September 18, 2025
GCF of 92 and 23
The GCF is the largest number that can divide two or more numbers without leaving any remainder. GCF is used to share items equally, to group or arrange items, and to schedule events. In this topic, we will learn about the GCF of 92 and 23.
What is the GCF of 92 and 23?
The greatest common factor of 92 and 23 is 23. 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 92 and 23?
To find the GCF of 92 and 23, a few methods are described below
- Listing Factors
- Prime Factorization
- Long Division Method / by Euclidean Algorithm
GCF of 92 and 23 by Using Listing of Factors
Steps to find the GCF of 92 and 23 using the listing of factors:
Step 1: Firstly, list the factors of each number
Factors of 92 = 1, 2, 4, 23, 46, 92.
Factors of 23 = 1, 23.
Step 2: Now, identify the common factors of them Common factors of 92 and 23: 1, 23.
Step 3: Choose the largest factor The largest factor that both numbers have is 23. The GCF of 92 and 23 is 23.
GCF of 92 and 23 Using Prime Factorization
To find the GCF of 92 and 23 using the Prime Factorization Method, follow these steps:
Step 1: Find the prime factors of each number
Prime Factors of 92: 92 = 2 × 2 × 23 = 2² × 23
Prime Factors of 23: 23 = 23¹ (since 23 is a prime number)
Step 2: Now, identify the common prime factors The common prime factor is 23.
Step 3: Multiply the common prime factors The greatest common factor of 92 and 23 is 23.
GCF of 92 and 23 Using Division Method or Euclidean Algorithm Method
Find the GCF of 92 and 23 using the division method or Euclidean Algorithm Method. Follow these steps:
Step 1: First, divide the larger number by the smaller number.
Here, divide 92 by 23. 92 ÷ 23 = 4 (quotient), remainder = 92 − (23×4) = 0.
The remainder is zero, so the divisor will become the GCF.
The GCF of 92 and 23 is 23.
Common Mistakes and How to Avoid Them in GCF of 92 and 23
Finding the GCF of 92 and 23 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 92, students may mention numbers like 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 indicates an incomplete understanding of the factors. Students should include 1 as a factor.
Mistake 4
Using Multiples Instead of Factors
Students confuse 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 the GCF of two numbers will always be an even number. But it's not true; 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 92 and 23 Examples
Problem 1
A gardener has 92 roses and 23 tulips. She wants to plant them in equal sets, with the largest number of plants in each set. How many plants will be in each set?
We should find the GCF of 92 and 23. The GCF of 92 and 23 is 23.
There are 23 equal sets. 92 ÷ 23 = 4.
23 ÷ 23 = 1.
There will be 23 sets, and each set has 4 roses and 1 tulip.
Explanation
As the GCF of 92 and 23 is 23, the gardener can make 23 sets.
Now divide 92 and 23 by 23.
Each set has 4 roses and 1 tulip.
Problem 2
A library has 92 fiction books and 23 non-fiction books. They want to arrange them in shelves with the same number of books on each shelf, using the largest possible number of books per shelf. How many books will be on each shelf?
GCF of 92 and 23 is 23. So each shelf will have 23 books.
Explanation
There are 92 fiction and 23 non-fiction books.
To find the total number of books on each shelf, we should find the GCF of 92 and 23.
There will be 23 books on each shelf.
Problem 3
A baker has 92 chocolate muffins and 23 vanilla muffins. She wants to pack both types of muffins into boxes of equal size, using the largest possible size. How many muffins should be in each box?
For calculating the largest equal size, we need to calculate the GCF of 92 and 23.
The GCF of 92 and 23 is 23.
Each box holds 23 muffins.
Explanation
To calculate the largest size of the muffin boxes, first we need to calculate the GCF of 92 and 23, which is 23.
Each box will hold 23 muffins.
Problem 4
A farmer has two fields, one 92 acres and the other 23 acres. He wants to divide them into the largest possible equal sections, without any land left over. What should be the size of each section?
The farmer needs the largest section of land. GCF of 92 and 23 is 23. The largest size of each section is 23 acres.
Explanation
To find the largest size of each section of the two fields, 92 acres and 23 acres, respectively, we have to find the GCF of 92 and 23, which is 23 acres.
The largest size of each section is 23 acres.
Problem 5
If the GCF of 92 and 'b' is 23, and the LCM is 184, find 'b'.
The value of 'b' is 46.
Explanation
GCF × LCM = product of the numbers
23 × 184 = 92 × b
4232 = 92b
b = 4232 ÷ 92 = 46
FAQs on the Greatest Common Factor of 92 and 23
1.What is the LCM of 92 and 23?
2.Is 92 divisible by 2?
3.What will be the GCF of any two prime numbers?
4.What is the prime factorization of 92?
5.Are 92 and 23 prime numbers?
Important Glossaries for GCF of 92 and 23
- Factors: Factors are numbers that divide the target number completely. For example, the factors of 46 are 1, 2, 23, and 46.
- Multiple: Multiples are the products we get by multiplying a given number by another. For example, the multiples of 23 are 23, 46, 69, 92, 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 46 are 2 and 23.
- Remainder: The value left after division when the number cannot be divided evenly. For example, when 92 is divided by 23, the remainder is 0.
- LCM: The smallest common multiple of two or more numbers is termed LCM. For example, the LCM of 92 and 23 is 92.
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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.
