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GCF of 3 and 20

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

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

What is GCF of 3 and 20?

Answer: GCF of 3 and 20 is 1.

Explanation:

The GCF of two non-zero integers, x(3) and y(20), is the greatest positive integer m(1) that divides both x(3) and y(20) without any remainder.

Methods to Find GCF of 3 and 20

The methods to find the GCF of 3 and 20 are explained below.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 3 and 20 by Long Division

GCF of 3 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

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

The corresponding divisor (1) is the GCF of 3 and 20.

GCF of 3 and 20 by Listing Common Factors

Factors of 3: 1, 3
Factors of 20: 1, 2, 4, 5, 10, 20

Since, 1 is the only common factor between 3 and 20. The Greatest Common Factor of 3 and 20 is 1.

GCF of 3 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 = 20 and Y = 3

GCF(20, 3) = GCF(3, 20 mod 3) = GCF(3, 2)
GCF(3, 2) = GCF(2, 3 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 3 and 20 is 1.

☛ Also Check:

GCF of 3 and 20 Examples

Example 1: For two numbers, GCF = 1 and LCM = 60. If one number is 20, find the other number.

Solution:

Given: GCF (x, 20) = 1 and LCM (x, 20) = 60
∵ GCF × LCM = 20 × (x)
⇒ x = (GCF × LCM)/20
⇒ x = (1 × 60)/20
⇒ x = 3
Therefore, the other number is 3.
Example 2: Find the GCF of 3 and 20, if their LCM is 60.

Solution:

∵ LCM × GCF = 3 × 20
⇒ GCF(3, 20) = (3 × 20)/60 = 1
Therefore, the greatest common factor of 3 and 20 is 1.
Example 3: The product of two numbers is 60. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 60
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 60/1
Therefore, the LCM is 60.

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FAQs on GCF of 3 and 20

What is the GCF of 3 and 20?

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

What is the Relation Between LCM and GCF of 3, 20?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 3 and 20, i.e. GCF × LCM = 3 × 20.

How to Find the GCF of 3 and 20 by Long Division Method?

To find the GCF of 3, 20 using long division method, 20 is divided by 3. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

If the GCF of 20 and 3 is 1, Find its LCM.

GCF(20, 3) × LCM(20, 3) = 20 × 3
Since the GCF of 20 and 3 = 1
⇒ 1 × LCM(20, 3) = 60
Therefore, LCM = 60
☛ GCF Calculator

What are the Methods to Find GCF of 3 and 20?

There are three commonly used methods to find the GCF of 3 and 20.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 3 and 20 by Prime Factorization?

To find the GCF of 3 and 20, we will find the prime factorization of the given numbers, i.e. 3 = 3; 20 = 2 × 2 × 5.
⇒ There is no common prime factor for 3 and 20. Hence, GCF (3, 20) = 1.
☛ What is a Prime Number?

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