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GCF of 20 and 30

GCF of 20 and 30 is the largest possible number that divides 20 and 30 exactly without any remainder. The factors of 20 and 30 are 1, 2, 4, 5, 10, 20 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 20 and 30 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 20 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 30?

Answer: GCF of 20 and 30 is 10.

Explanation:

The GCF of two non-zero integers, x(20) and y(30), is the greatest positive integer m(10) that divides both x(20) and y(30) without any remainder.

Methods to Find GCF of 20 and 30

The methods to find the GCF of 20 and 30 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Long Division Method

GCF of 20 and 30 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 = 30 and Y = 20

GCF(30, 20) = GCF(20, 30 mod 20) = GCF(20, 10)
GCF(20, 10) = GCF(10, 20 mod 10) = GCF(10, 0)
GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 20 and 30 is 10.

GCF of 20 and 30 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 4 common factors of 20 and 30, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 20 and 30 is 10.

GCF of 20 and 30 by Long Division

GCF of 20 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (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 30.

☛ Also Check:

GCF of 20 and 30 Examples

Example 1: For two numbers, GCF = 10 and LCM = 60. If one number is 30, find the other number.

Solution:

Given: GCF (y, 30) = 10 and LCM (y, 30) = 60
∵ GCF × LCM = 30 × (y)
⇒ y = (GCF × LCM)/30
⇒ y = (10 × 60)/30
⇒ y = 20
Therefore, the other number is 20.
Example 2: Find the GCF of 20 and 30, if their LCM is 60.

Solution:

∵ LCM × GCF = 20 × 30
⇒ GCF(20, 30) = (20 × 30)/60 = 10
Therefore, the greatest common factor of 20 and 30 is 10.
Example 3: Find the greatest number that divides 20 and 30 exactly.

Solution:

The greatest number that divides 20 and 30 exactly is their greatest common factor, i.e. GCF of 20 and 30.
⇒ Factors of 20 and 30:
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 20 and 30 is 10.

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FAQs on GCF of 20 and 30

What is the GCF of 20 and 30?

The GCF of 20 and 30 is 10. To calculate the GCF of 20 and 30, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 20 and 30, i.e., 10.

How to Find the GCF of 20 and 30 by Long Division Method?

To find the GCF of 20, 30 using long division method, 30 is divided by 20. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

How to Find the GCF of 20 and 30 by Prime Factorization?

To find the GCF of 20 and 30, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 30 = 2 × 3 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 20 and 30. Hence, GCF(20, 30) = 2 × 5 = 10
☛ What are Prime Numbers?

What are the Methods to Find GCF of 20 and 30?

There are three commonly used methods to find the GCF of 20 and 30.

By Listing Common Factors
By Long Division
By Prime Factorization

If the GCF of 30 and 20 is 10, Find its LCM.

GCF(30, 20) × LCM(30, 20) = 30 × 20
Since the GCF of 30 and 20 = 10
⇒ 10 × LCM(30, 20) = 600
Therefore, LCM = 60
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 20, 30?

The following equation can be used to express the relation between LCM and GCF of 20 and 30, i.e. GCF × LCM = 20 × 30.

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