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GCF of 75 and 20

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

1.	GCF of 75 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 75 and 20?

Answer: GCF of 75 and 20 is 5.

Explanation:

The GCF of two non-zero integers, x(75) and y(20), is the greatest positive integer m(5) that divides both x(75) and y(20) without any remainder.

Methods to Find GCF of 75 and 20

The methods to find the GCF of 75 and 20 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 75 and 20 by Prime Factorization

Prime factorization of 75 and 20 is (3 × 5 × 5) and (2 × 2 × 5) respectively. As visible, 75 and 20 have only one common prime factor i.e. 5. Hence, the GCF of 75 and 20 is 5.

GCF of 75 and 20 by Long Division

GCF of 75 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 75 (larger number) by 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (15).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 75 and 20.

GCF of 75 and 20 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 = 20

GCF(75, 20) = GCF(20, 75 mod 20) = GCF(20, 15)
GCF(20, 15) = GCF(15, 20 mod 15) = GCF(15, 5)
GCF(15, 5) = GCF(5, 15 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 75 and 20 is 5.

☛ Also Check:

GCF of 75 and 20 Examples

Example 1: For two numbers, GCF = 5 and LCM = 300. If one number is 75, find the other number.

Solution:

Given: GCF (y, 75) = 5 and LCM (y, 75) = 300
∵ GCF × LCM = 75 × (y)
⇒ y = (GCF × LCM)/75
⇒ y = (5 × 300)/75
⇒ y = 20
Therefore, the other number is 20.
Example 2: Find the greatest number that divides 75 and 20 exactly.

Solution:

The greatest number that divides 75 and 20 exactly is their greatest common factor, i.e. GCF of 75 and 20.
⇒ Factors of 75 and 20:
- Factors of 75 = 1, 3, 5, 15, 25, 75
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 75 and 20 is 5.
Example 3: Find the GCF of 75 and 20, if their LCM is 300.

Solution:

∵ LCM × GCF = 75 × 20
⇒ GCF(75, 20) = (75 × 20)/300 = 5
Therefore, the greatest common factor of 75 and 20 is 5.

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FAQs on GCF of 75 and 20

What is the GCF of 75 and 20?

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

How to Find the GCF of 75 and 20 by Prime Factorization?

To find the GCF of 75 and 20, we will find the prime factorization of the given numbers, i.e. 75 = 3 × 5 × 5; 20 = 2 × 2 × 5.
⇒ Since 5 is the only common prime factor of 75 and 20. Hence, GCF (75, 20) = 5.
☛ Prime Number

What are the Methods to Find GCF of 75 and 20?

There are three commonly used methods to find the GCF of 75 and 20.

By Long Division
By Euclidean Algorithm
By Prime Factorization

If the GCF of 20 and 75 is 5, Find its LCM.

GCF(20, 75) × LCM(20, 75) = 20 × 75
Since the GCF of 20 and 75 = 5
⇒ 5 × LCM(20, 75) = 1500
Therefore, LCM = 300
☛ Greatest Common Factor Calculator

How to Find the GCF of 75 and 20 by Long Division Method?

To find the GCF of 75, 20 using long division method, 75 is divided by 20. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 75, 20?

The following equation can be used to express the relation between Least Common Multiple and GCF of 75 and 20, i.e. GCF × LCM = 75 × 20.

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