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GCF of 80 and 20

GCF of 80 and 20 is the largest possible number that divides 80 and 20 exactly without any remainder. The factors of 80 and 20 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the GCF of 80 and 20 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 80 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 80 and 20?

Answer: GCF of 80 and 20 is 20.

Explanation:

The GCF of two non-zero integers, x(80) and y(20), is the greatest positive integer m(20) that divides both x(80) and y(20) without any remainder.

Methods to Find GCF of 80 and 20

The methods to find the GCF of 80 and 20 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 80 and 20 by Listing Common Factors

Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Factors of 20: 1, 2, 4, 5, 10, 20

There are 6 common factors of 80 and 20, that are 1, 2, 4, 5, 10, and 20. Therefore, the greatest common factor of 80 and 20 is 20.

GCF of 80 and 20 by Prime Factorization

Prime factorization of 80 and 20 is (2 × 2 × 2 × 2 × 5) and (2 × 2 × 5) respectively. As visible, 80 and 20 have common prime factors. Hence, the GCF of 80 and 20 is 2 × 2 × 5 = 20.

GCF of 80 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 = 80 and Y = 20

GCF(80, 20) = GCF(20, 80 mod 20) = GCF(20, 0)
GCF(20, 0) = 20 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 80 and 20 is 20.

☛ Also Check:

GCF of 80 and 20 Examples

Example 1: The product of two numbers is 1600. If their GCF is 20, what is their LCM?

Solution:

Given: GCF = 20 and product of numbers = 1600
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1600/20
Therefore, the LCM is 80.
Example 2: Find the GCF of 80 and 20, if their LCM is 80.

Solution:

∵ LCM × GCF = 80 × 20
⇒ GCF(80, 20) = (80 × 20)/80 = 20
Therefore, the greatest common factor of 80 and 20 is 20.
Example 3: Find the greatest number that divides 80 and 20 exactly.

Solution:

The greatest number that divides 80 and 20 exactly is their greatest common factor, i.e. GCF of 80 and 20.
⇒ Factors of 80 and 20:
- Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 80 and 20 is 20.

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FAQs on GCF of 80 and 20

What is the GCF of 80 and 20?

The GCF of 80 and 20 is 20. To calculate the greatest common factor of 80 and 20, we need to factor each number (factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides both 80 and 20, i.e., 20.

If the GCF of 20 and 80 is 20, Find its LCM.

GCF(20, 80) × LCM(20, 80) = 20 × 80
Since the GCF of 20 and 80 = 20
⇒ 20 × LCM(20, 80) = 1600
Therefore, LCM = 80
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 80, 20?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 80 and 20, i.e. GCF × LCM = 80 × 20.

How to Find the GCF of 80 and 20 by Prime Factorization?

To find the GCF of 80 and 20, we will find the prime factorization of the given numbers, i.e. 80 = 2 × 2 × 2 × 2 × 5; 20 = 2 × 2 × 5.
⇒ Since 2, 2, 5 are common terms in the prime factorization of 80 and 20. Hence, GCF(80, 20) = 2 × 2 × 5 = 20
☛ Prime Number

How to Find the GCF of 80 and 20 by Long Division Method?

To find the GCF of 80, 20 using long division method, 80 is divided by 20. The corresponding divisor (20) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 80 and 20?

There are three commonly used methods to find the GCF of 80 and 20.

By Euclidean Algorithm
By Prime Factorization
By Long Division

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