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GCF of 20 and 50

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

1.	GCF of 20 and 50
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 50?

Answer: GCF of 20 and 50 is 10.

Explanation:

The GCF of two non-zero integers, x(20) and y(50), is the greatest positive integer m(10) that divides both x(20) and y(50) without any remainder.

Methods to Find GCF of 20 and 50

The methods to find the GCF of 20 and 50 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 20 and 50 by Listing Common Factors

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

There are 4 common factors of 20 and 50, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 20 and 50 is 10.

GCF of 20 and 50 by Long Division

GCF of 20 and 50 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 50 (larger number) by 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (10).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (10) is the GCF of 20 and 50.

GCF of 20 and 50 by Prime Factorization

Prime factorization of 20 and 50 is (2 × 2 × 5) and (2 × 5 × 5) respectively. As visible, 20 and 50 have common prime factors. Hence, the GCF of 20 and 50 is 2 × 5 = 10.

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GCF of 20 and 50 Examples

Example 1: Find the greatest number that divides 20 and 50 exactly.

Solution:

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

Solution:

Given: GCF (z, 50) = 10 and LCM (z, 50) = 100
∵ GCF × LCM = 50 × (z)
⇒ z = (GCF × LCM)/50
⇒ z = (10 × 100)/50
⇒ z = 20
Therefore, the other number is 20.
Example 3: Find the GCF of 20 and 50, if their LCM is 100.

Solution:

∵ LCM × GCF = 20 × 50
⇒ GCF(20, 50) = (20 × 50)/100 = 10
Therefore, the greatest common factor of 20 and 50 is 10.

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FAQs on GCF of 20 and 50

What is the GCF of 20 and 50?

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

How to Find the GCF of 20 and 50 by Prime Factorization?

To find the GCF of 20 and 50, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 50 = 2 × 5 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 20 and 50. Hence, GCF(20, 50) = 2 × 5 = 10
☛ Prime Number

What are the Methods to Find GCF of 20 and 50?

There are three commonly used methods to find the GCF of 20 and 50.

By Prime Factorization
By Listing Common Factors
By Long Division

If the GCF of 50 and 20 is 10, Find its LCM.

GCF(50, 20) × LCM(50, 20) = 50 × 20
Since the GCF of 50 and 20 = 10
⇒ 10 × LCM(50, 20) = 1000
Therefore, LCM = 100
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How to Find the GCF of 20 and 50 by Long Division Method?

To find the GCF of 20, 50 using long division method, 50 is divided by 20. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 20, 50?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 20 and 50, i.e. GCF × LCM = 20 × 50.

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