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GCF of 5 and 30

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

1.	GCF of 5 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 5 and 30?

Answer: GCF of 5 and 30 is 5.

Explanation:

The GCF of two non-zero integers, x(5) and y(30), is the greatest positive integer m(5) that divides both x(5) and y(30) without any remainder.

Methods to Find GCF of 5 and 30

The methods to find the GCF of 5 and 30 are explained below.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 5 and 30 by Prime Factorization

Prime factorization of 5 and 30 is (5) and (2 × 3 × 5) respectively. As visible, 5 and 30 have only one common prime factor i.e. 5. Hence, the GCF of 5 and 30 is 5.

GCF of 5 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 = 5

GCF(30, 5) = GCF(5, 30 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 5 and 30 is 5.

GCF of 5 and 30 by Listing Common Factors

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

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

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GCF of 5 and 30 Examples

Example 1: Find the greatest number that divides 5 and 30 exactly.

Solution:

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

Solution:

∵ LCM × GCF = 5 × 30
⇒ GCF(5, 30) = (5 × 30)/30 = 5
Therefore, the greatest common factor of 5 and 30 is 5.
Example 3: For two numbers, GCF = 5 and LCM = 30. If one number is 30, find the other number.

Solution:

Given: GCF (z, 30) = 5 and LCM (z, 30) = 30
∵ GCF × LCM = 30 × (z)
⇒ z = (GCF × LCM)/30
⇒ z = (5 × 30)/30
⇒ z = 5
Therefore, the other number is 5.

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FAQs on GCF of 5 and 30

What is the GCF of 5 and 30?

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

How to Find the GCF of 5 and 30 by Long Division Method?

To find the GCF of 5, 30 using long division method, 30 is divided by 5. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

If the GCF of 30 and 5 is 5, Find its LCM.

GCF(30, 5) × LCM(30, 5) = 30 × 5
Since the GCF of 30 and 5 = 5
⇒ 5 × LCM(30, 5) = 150
Therefore, LCM = 30
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What is the Relation Between LCM and GCF of 5, 30?

The following equation can be used to express the relation between Least Common Multiple and GCF of 5 and 30, i.e. GCF × LCM = 5 × 30.

What are the Methods to Find GCF of 5 and 30?

There are three commonly used methods to find the GCF of 5 and 30.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the GCF of 5 and 30 by Prime Factorization?

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

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