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GCF of 80 and 100

GCF of 80 and 100 is the largest possible number that divides 80 and 100 exactly without any remainder. The factors of 80 and 100 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 and 1, 2, 4, 5, 10, 20, 25, 50, 100 respectively. There are 3 commonly used methods to find the GCF of 80 and 100 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 80 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 80 and 100?

Answer: GCF of 80 and 100 is 20.

Explanation:

The GCF of two non-zero integers, x(80) and y(100), is the greatest positive integer m(20) that divides both x(80) and y(100) without any remainder.

Methods to Find GCF of 80 and 100

Let's look at the different methods for finding the GCF of 80 and 100.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 80 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 = 80

GCF(100, 80) = GCF(80, 100 mod 80) = GCF(80, 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 100 is 20.

GCF of 80 and 100 by Prime Factorization

Prime factorization of 80 and 100 is (2 × 2 × 2 × 2 × 5) and (2 × 2 × 5 × 5) respectively. As visible, 80 and 100 have common prime factors. Hence, the GCF of 80 and 100 is 2 × 2 × 5 = 20.

GCF of 80 and 100 by Long Division

GCF of 80 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 80 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (80) by the remainder (20).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (20) is the GCF of 80 and 100.

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GCF of 80 and 100 Examples

Example 1: The product of two numbers is 8000. If their GCF is 20, what is their LCM?

Solution:

Given: GCF = 20 and product of numbers = 8000
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 8000/20
Therefore, the LCM is 400.
Example 2: Find the greatest number that divides 80 and 100 exactly.

Solution:

The greatest number that divides 80 and 100 exactly is their greatest common factor, i.e. GCF of 80 and 100.
⇒ Factors of 80 and 100:
- Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
- Factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100
Therefore, the GCF of 80 and 100 is 20.
Example 3: For two numbers, GCF = 20 and LCM = 400. If one number is 80, find the other number.

Solution:

Given: GCF (x, 80) = 20 and LCM (x, 80) = 400
∵ GCF × LCM = 80 × (x)
⇒ x = (GCF × LCM)/80
⇒ x = (20 × 400)/80
⇒ x = 100
Therefore, the other number is 100.

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FAQs on GCF of 80 and 100

What is the GCF of 80 and 100?

The GCF of 80 and 100 is 20. To calculate the greatest common factor (GCF) of 80 and 100, we need to factor each number (factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80; factors of 100 = 1, 2, 4, 5, 10, 20, 25, 50, 100) and choose the greatest factor that exactly divides both 80 and 100, i.e., 20.

If the GCF of 100 and 80 is 20, Find its LCM.

GCF(100, 80) × LCM(100, 80) = 100 × 80
Since the GCF of 100 and 80 = 20
⇒ 20 × LCM(100, 80) = 8000
Therefore, LCM = 400
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What are the Methods to Find GCF of 80 and 100?

There are three commonly used methods to find the GCF of 80 and 100.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 80 and 100 by Prime Factorization?

To find the GCF of 80 and 100, we will find the prime factorization of the given numbers, i.e. 80 = 2 × 2 × 2 × 2 × 5; 100 = 2 × 2 × 5 × 5.
⇒ Since 2, 2, 5 are common terms in the prime factorization of 80 and 100. Hence, GCF(80, 100) = 2 × 2 × 5 = 20
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 80, 100?

The following equation can be used to express the relation between Least Common Multiple and GCF of 80 and 100, i.e. GCF × LCM = 80 × 100.

How to Find the GCF of 80 and 100 by Long Division Method?

To find the GCF of 80, 100 using long division method, 100 is divided by 80. The corresponding divisor (20) when remainder equals 0 is taken as GCF.

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