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GCF of 50 and 75

GCF of 50 and 75 is the largest possible number that divides 50 and 75 exactly without any remainder. The factors of 50 and 75 are 1, 2, 5, 10, 25, 50 and 1, 3, 5, 15, 25, 75 respectively. There are 3 commonly used methods to find the GCF of 50 and 75 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 50 and 75
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 50 and 75?

Answer: GCF of 50 and 75 is 25.

Explanation:

The GCF of two non-zero integers, x(50) and y(75), is the greatest positive integer m(25) that divides both x(50) and y(75) without any remainder.

Methods to Find GCF of 50 and 75

Let's look at the different methods for finding the GCF of 50 and 75.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 50 and 75 by Prime Factorization

Prime factorization of 50 and 75 is (2 × 5 × 5) and (3 × 5 × 5) respectively. As visible, 50 and 75 have common prime factors. Hence, the GCF of 50 and 75 is 5 × 5 = 25.

GCF of 50 and 75 by Long Division

GCF of 50 and 75 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 75 (larger number) by 50 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (50) by the remainder (25).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (25) is the GCF of 50 and 75.

GCF of 50 and 75 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 = 75 and Y = 50

GCF(75, 50) = GCF(50, 75 mod 50) = GCF(50, 25)
GCF(50, 25) = GCF(25, 50 mod 25) = GCF(25, 0)
GCF(25, 0) = 25 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 50 and 75 is 25.

☛ Also Check:

GCF of 50 and 75 Examples

Example 1: Find the greatest number that divides 50 and 75 exactly.

Solution:

The greatest number that divides 50 and 75 exactly is their greatest common factor, i.e. GCF of 50 and 75.
⇒ Factors of 50 and 75:
- Factors of 50 = 1, 2, 5, 10, 25, 50
- Factors of 75 = 1, 3, 5, 15, 25, 75
Therefore, the GCF of 50 and 75 is 25.
Example 2: Find the GCF of 50 and 75, if their LCM is 150.

Solution:

∵ LCM × GCF = 50 × 75
⇒ GCF(50, 75) = (50 × 75)/150 = 25
Therefore, the greatest common factor of 50 and 75 is 25.
Example 3: For two numbers, GCF = 25 and LCM = 150. If one number is 75, find the other number.

Solution:

Given: GCF (x, 75) = 25 and LCM (x, 75) = 150
∵ GCF × LCM = 75 × (x)
⇒ x = (GCF × LCM)/75
⇒ x = (25 × 150)/75
⇒ x = 50
Therefore, the other number is 50.

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FAQs on GCF of 50 and 75

What is the GCF of 50 and 75?

The GCF of 50 and 75 is 25. To calculate the GCF of 50 and 75, we need to factor each number (factors of 50 = 1, 2, 5, 10, 25, 50; factors of 75 = 1, 3, 5, 15, 25, 75) and choose the greatest factor that exactly divides both 50 and 75, i.e., 25.

How to Find the GCF of 50 and 75 by Prime Factorization?

To find the GCF of 50 and 75, we will find the prime factorization of the given numbers, i.e. 50 = 2 × 5 × 5; 75 = 3 × 5 × 5.
⇒ Since 5, 5 are common terms in the prime factorization of 50 and 75. Hence, GCF(50, 75) = 5 × 5 = 25
☛ Prime Numbers

What are the Methods to Find GCF of 50 and 75?

There are three commonly used methods to find the GCF of 50 and 75.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 50 and 75 by Long Division Method?

To find the GCF of 50, 75 using long division method, 75 is divided by 50. The corresponding divisor (25) when remainder equals 0 is taken as GCF.

If the GCF of 75 and 50 is 25, Find its LCM.

GCF(75, 50) × LCM(75, 50) = 75 × 50
Since the GCF of 75 and 50 = 25
⇒ 25 × LCM(75, 50) = 3750
Therefore, LCM = 150
☛ GCF Calculator

What is the Relation Between LCM and GCF of 50, 75?

The following equation can be used to express the relation between Least Common Multiple and GCF of 50 and 75, i.e. GCF × LCM = 50 × 75.

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