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GCF of 20 and 100

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

1.	GCF of 20 and 100
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 100?

Answer: GCF of 20 and 100 is 20.

Explanation:

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

Methods to Find GCF of 20 and 100

The methods to find the GCF of 20 and 100 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 20 and 100 by Prime Factorization

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

GCF of 20 and 100 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

There are 6 common factors of 20 and 100, that are 1, 2, 4, 5, 10, and 20. Therefore, the greatest common factor of 20 and 100 is 20.

GCF of 20 and 100 by Long Division

GCF of 20 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 20 (smaller number).
Step 2: Since the remainder = 0, the divisor (20) is the GCF of 20 and 100.

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

☛ Also Check:

GCF of 20 and 100 Examples

Example 1: Find the GCF of 20 and 100, if their LCM is 100.

Solution:

∵ LCM × GCF = 20 × 100
⇒ GCF(20, 100) = (20 × 100)/100 = 20
Therefore, the greatest common factor of 20 and 100 is 20.
Example 2: Find the greatest number that divides 20 and 100 exactly.

Solution:

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

Solution:

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

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FAQs on GCF of 20 and 100

What is the GCF of 20 and 100?

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

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

GCF(100, 20) × LCM(100, 20) = 100 × 20
Since the GCF of 100 and 20 = 20
⇒ 20 × LCM(100, 20) = 2000
Therefore, LCM = 100
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 20, 100?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 20 and 100, i.e. GCF × LCM = 20 × 100.

How to Find the GCF of 20 and 100 by Prime Factorization?

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

What are the Methods to Find GCF of 20 and 100?

There are three commonly used methods to find the GCF of 20 and 100.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 20 and 100 by Long Division Method?

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

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