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GCF of 75 and 100

GCF of 75 and 100 is the largest possible number that divides 75 and 100 exactly without any remainder. The factors of 75 and 100 are 1, 3, 5, 15, 25, 75 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 75 and 100 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 75 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 75 and 100?

Answer: GCF of 75 and 100 is 25.

Explanation:

The GCF of two non-zero integers, x(75) and y(100), is the greatest positive integer m(25) that divides both x(75) and y(100) without any remainder.

Methods to Find GCF of 75 and 100

The methods to find the GCF of 75 and 100 are explained below.

Long Division Method
Prime Factorization Method
Using Euclid's Algorithm

GCF of 75 and 100 by Long Division

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

The corresponding divisor (25) is the GCF of 75 and 100.

GCF of 75 and 100 by Prime Factorization

Prime factorization of 75 and 100 is (3 × 5 × 5) and (2 × 2 × 5 × 5) respectively. As visible, 75 and 100 have common prime factors. Hence, the GCF of 75 and 100 is 5 × 5 = 25.

GCF of 75 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 = 75

GCF(100, 75) = GCF(75, 100 mod 75) = GCF(75, 25)
GCF(75, 25) = GCF(25, 75 mod 25) = GCF(25, 0)
GCF(25, 0) = 25 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 75 and 100 is 25.

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GCF of 75 and 100 Examples

Example 1: The product of two numbers is 7500. If their GCF is 25, what is their LCM?

Solution:

Given: GCF = 25 and product of numbers = 7500
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 7500/25
Therefore, the LCM is 300.
Example 2: Find the greatest number that divides 75 and 100 exactly.

Solution:

The greatest number that divides 75 and 100 exactly is their greatest common factor, i.e. GCF of 75 and 100.
⇒ Factors of 75 and 100:
- Factors of 75 = 1, 3, 5, 15, 25, 75
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 75 and 100 is 25.
Example 3: For two numbers, GCF = 25 and LCM = 300. If one number is 75, find the other number.

Solution:

Given: GCF (z, 75) = 25 and LCM (z, 75) = 300
∵ GCF × LCM = 75 × (z)
⇒ z = (GCF × LCM)/75
⇒ z = (25 × 300)/75
⇒ z = 100
Therefore, the other number is 100.

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FAQs on GCF of 75 and 100

What is the GCF of 75 and 100?

The GCF of 75 and 100 is 25. To calculate the greatest common factor (GCF) of 75 and 100, we need to factor each number (factors of 75 = 1, 3, 5, 15, 25, 75; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 75 and 100, i.e., 25.

How to Find the GCF of 75 and 100 by Prime Factorization?

To find the GCF of 75 and 100, we will find the prime factorization of the given numbers, i.e. 75 = 3 × 5 × 5; 100 = 2 × 2 × 5 × 5.
⇒ Since 5, 5 are common terms in the prime factorization of 75 and 100. Hence, GCF(75, 100) = 5 × 5 = 25
☛ What is a Prime Number?

How to Find the GCF of 75 and 100 by Long Division Method?

To find the GCF of 75, 100 using long division method, 100 is divided by 75. The corresponding divisor (25) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 75, 100?

The following equation can be used to express the relation between Least Common Multiple and GCF of 75 and 100, i.e. GCF × LCM = 75 × 100.

If the GCF of 100 and 75 is 25, Find its LCM.

GCF(100, 75) × LCM(100, 75) = 100 × 75
Since the GCF of 100 and 75 = 25
⇒ 25 × LCM(100, 75) = 7500
Therefore, LCM = 300
☛ GCF Calculator

What are the Methods to Find GCF of 75 and 100?

There are three commonly used methods to find the GCF of 75 and 100.

By Euclidean Algorithm
By Long Division
By Prime Factorization

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