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GCF of 3 and 30

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

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

What is GCF of 3 and 30?

Answer: GCF of 3 and 30 is 3.

Explanation:

The GCF of two non-zero integers, x(3) and y(30), is the greatest positive integer m(3) that divides both x(3) and y(30) without any remainder.

Methods to Find GCF of 3 and 30

Let's look at the different methods for finding the GCF of 3 and 30.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 3 and 30 by Long Division

GCF of 3 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 3 (smaller number).
Step 2: Since the remainder = 0, the divisor (3) is the GCF of 3 and 30.

The corresponding divisor (3) is the GCF of 3 and 30.

GCF of 3 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 = 3

GCF(30, 3) = GCF(3, 30 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 3 and 30 is 3.

GCF of 3 and 30 by Listing Common Factors

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

There are 2 common factors of 3 and 30, that are 1 and 3. Therefore, the greatest common factor of 3 and 30 is 3.

☛ Also Check:

GCF of 3 and 30 Examples

Example 1: For two numbers, GCF = 3 and LCM = 30. If one number is 30, find the other number.

Solution:

Given: GCF (y, 30) = 3 and LCM (y, 30) = 30
∵ GCF × LCM = 30 × (y)
⇒ y = (GCF × LCM)/30
⇒ y = (3 × 30)/30
⇒ y = 3
Therefore, the other number is 3.
Example 2: Find the greatest number that divides 3 and 30 exactly.

Solution:

The greatest number that divides 3 and 30 exactly is their greatest common factor, i.e. GCF of 3 and 30.
⇒ Factors of 3 and 30:
- Factors of 3 = 1, 3
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 3 and 30 is 3.
Example 3: The product of two numbers is 90. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 90
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 90/3
Therefore, the LCM is 30.

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FAQs on GCF of 3 and 30

What is the GCF of 3 and 30?

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

What is the Relation Between LCM and GCF of 3, 30?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 3 and 30, i.e. GCF × LCM = 3 × 30.

If the GCF of 30 and 3 is 3, Find its LCM.

GCF(30, 3) × LCM(30, 3) = 30 × 3
Since the GCF of 30 and 3 = 3
⇒ 3 × LCM(30, 3) = 90
Therefore, LCM = 30
☛ GCF Calculator

What are the Methods to Find GCF of 3 and 30?

There are three commonly used methods to find the GCF of 3 and 30.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 3 and 30 by Long Division Method?

To find the GCF of 3, 30 using long division method, 30 is divided by 3. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

How to Find the GCF of 3 and 30 by Prime Factorization?

To find the GCF of 3 and 30, we will find the prime factorization of the given numbers, i.e. 3 = 3; 30 = 2 × 3 × 5.
⇒ Since 3 is the only common prime factor of 3 and 30. Hence, GCF (3, 30) = 3.
☛ Prime Number

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