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GCF of 50 and 100

GCF of 50 and 100 is the largest possible number that divides 50 and 100 exactly without any remainder. The factors of 50 and 100 are 1, 2, 5, 10, 25, 50 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 50 and 100 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 50 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 50 and 100?

Answer: GCF of 50 and 100 is 50.

Explanation:

The GCF of two non-zero integers, x(50) and y(100), is the greatest positive integer m(50) that divides both x(50) and y(100) without any remainder.

Methods to Find GCF of 50 and 100

The methods to find the GCF of 50 and 100 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 50 and 100 by Long Division

GCF of 50 and 100 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 100 (larger number) by 50 (smaller number).
Step 2: Since the remainder = 0, the divisor (50) is the GCF of 50 and 100.

The corresponding divisor (50) is the GCF of 50 and 100.

GCF of 50 and 100 by Listing Common Factors

Factors of 50: 1, 2, 5, 10, 25, 50
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 6 common factors of 50 and 100, that are 1, 2, 5, 10, 50, and 25. Therefore, the greatest common factor of 50 and 100 is 50.

GCF of 50 and 100 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 = 100 and Y = 50

GCF(100, 50) = GCF(50, 100 mod 50) = GCF(50, 0)
GCF(50, 0) = 50 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 50 and 100 is 50.

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GCF of 50 and 100 Examples

Example 1: Find the greatest number that divides 50 and 100 exactly.

Solution:

The greatest number that divides 50 and 100 exactly is their greatest common factor, i.e. GCF of 50 and 100.
⇒ Factors of 50 and 100:
- Factors of 50 = 1, 2, 5, 10, 25, 50
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 50 and 100 is 50.
Example 2: The product of two numbers is 5000. If their GCF is 50, what is their LCM?

Solution:

Given: GCF = 50 and product of numbers = 5000
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 5000/50
Therefore, the LCM is 100.
Example 3: For two numbers, GCF = 50 and LCM = 100. If one number is 100, find the other number.

Solution:

Given: GCF (y, 100) = 50 and LCM (y, 100) = 100
∵ GCF × LCM = 100 × (y)
⇒ y = (GCF × LCM)/100
⇒ y = (50 × 100)/100
⇒ y = 50
Therefore, the other number is 50.

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FAQs on GCF of 50 and 100

What is the GCF of 50 and 100?

The GCF of 50 and 100 is 50. To calculate the GCF (Greatest Common Factor) of 50 and 100, we need to factor each number (factors of 50 = 1, 2, 5, 10, 25, 50; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 50 and 100, i.e., 50.

What are the Methods to Find GCF of 50 and 100?

There are three commonly used methods to find the GCF of 50 and 100.

By Long Division
By Euclidean Algorithm
By Prime Factorization

How to Find the GCF of 50 and 100 by Long Division Method?

To find the GCF of 50, 100 using long division method, 100 is divided by 50. The corresponding divisor (50) when remainder equals 0 is taken as GCF.

How to Find the GCF of 50 and 100 by Prime Factorization?

To find the GCF of 50 and 100, we will find the prime factorization of the given numbers, i.e. 50 = 2 × 5 × 5; 100 = 2 × 2 × 5 × 5.
⇒ Since 2, 5, 5 are common terms in the prime factorization of 50 and 100. Hence, GCF(50, 100) = 2 × 5 × 5 = 50
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 50, 100?

The following equation can be used to express the relation between LCM and GCF of 50 and 100, i.e. GCF × LCM = 50 × 100.

If the GCF of 100 and 50 is 50, Find its LCM.

GCF(100, 50) × LCM(100, 50) = 100 × 50
Since the GCF of 100 and 50 = 50
⇒ 50 × LCM(100, 50) = 5000
Therefore, LCM = 100
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