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GCF of 92 and 23

GCF of 92 and 23 is the largest possible number that divides 92 and 23 exactly without any remainder. The factors of 92 and 23 are 1, 2, 4, 23, 46, 92 and 1, 23 respectively. There are 3 commonly used methods to find the GCF of 92 and 23 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 92 and 23
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 92 and 23?

Answer: GCF of 92 and 23 is 23.

Explanation:

The GCF of two non-zero integers, x(92) and y(23), is the greatest positive integer m(23) that divides both x(92) and y(23) without any remainder.

Methods to Find GCF of 92 and 23

Let's look at the different methods for finding the GCF of 92 and 23.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 92 and 23 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 92 and Y = 23

GCF(92, 23) = GCF(23, 92 mod 23) = GCF(23, 0)
GCF(23, 0) = 23 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 92 and 23 is 23.

GCF of 92 and 23 by Long Division

GCF of 92 and 23 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 92 (larger number) by 23 (smaller number).
Step 2: Since the remainder = 0, the divisor (23) is the GCF of 92 and 23.

The corresponding divisor (23) is the GCF of 92 and 23.

GCF of 92 and 23 by Prime Factorization

Prime factorization of 92 and 23 is (2 × 2 × 23) and (23) respectively. As visible, 92 and 23 have only one common prime factor i.e. 23. Hence, the GCF of 92 and 23 is 23.

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GCF of 92 and 23 Examples

Example 1: For two numbers, GCF = 23 and LCM = 92. If one number is 92, find the other number.

Solution:

Given: GCF (x, 92) = 23 and LCM (x, 92) = 92
∵ GCF × LCM = 92 × (x)
⇒ x = (GCF × LCM)/92
⇒ x = (23 × 92)/92
⇒ x = 23
Therefore, the other number is 23.
Example 2: Find the GCF of 92 and 23, if their LCM is 92.

Solution:

∵ LCM × GCF = 92 × 23
⇒ GCF(92, 23) = (92 × 23)/92 = 23
Therefore, the greatest common factor of 92 and 23 is 23.
Example 3: The product of two numbers is 2116. If their GCF is 23, what is their LCM?

Solution:

Given: GCF = 23 and product of numbers = 2116
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2116/23
Therefore, the LCM is 92.

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FAQs on GCF of 92 and 23

What is the GCF of 92 and 23?

The GCF of 92 and 23 is 23. To calculate the GCF (Greatest Common Factor) of 92 and 23, we need to factor each number (factors of 92 = 1, 2, 4, 23, 46, 92; factors of 23 = 1, 23) and choose the greatest factor that exactly divides both 92 and 23, i.e., 23.

What are the Methods to Find GCF of 92 and 23?

There are three commonly used methods to find the GCF of 92 and 23.

By Listing Common Factors
By Prime Factorization
By Long Division

How to Find the GCF of 92 and 23 by Long Division Method?

To find the GCF of 92, 23 using long division method, 92 is divided by 23. The corresponding divisor (23) when remainder equals 0 is taken as GCF.

If the GCF of 23 and 92 is 23, Find its LCM.

GCF(23, 92) × LCM(23, 92) = 23 × 92
Since the GCF of 23 and 92 = 23
⇒ 23 × LCM(23, 92) = 2116
Therefore, LCM = 92
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What is the Relation Between LCM and GCF of 92, 23?

The following equation can be used to express the relation between LCM and GCF of 92 and 23, i.e. GCF × LCM = 92 × 23.

How to Find the GCF of 92 and 23 by Prime Factorization?

To find the GCF of 92 and 23, we will find the prime factorization of the given numbers, i.e. 92 = 2 × 2 × 23; 23 = 23.
⇒ Since 23 is the only common prime factor of 92 and 23. Hence, GCF (92, 23) = 23.
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