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GCF of 30 and 60

GCF of 30 and 60 is the largest possible number that divides 30 and 60 exactly without any remainder. The factors of 30 and 60 are 1, 2, 3, 5, 6, 10, 15, 30 and 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 respectively. There are 3 commonly used methods to find the GCF of 30 and 60 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 30 and 60
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 30 and 60?

Answer: GCF of 30 and 60 is 30.

Explanation:

The GCF of two non-zero integers, x(30) and y(60), is the greatest positive integer m(30) that divides both x(30) and y(60) without any remainder.

Methods to Find GCF of 30 and 60

The methods to find the GCF of 30 and 60 are explained below.

Using Euclid's Algorithm
Listing Common Factors
Prime Factorization Method

GCF of 30 and 60 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 = 60 and Y = 30

GCF(60, 30) = GCF(30, 60 mod 30) = GCF(30, 0)
GCF(30, 0) = 30 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 30 and 60 is 30.

GCF of 30 and 60 by Listing Common Factors

Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

There are 8 common factors of 30 and 60, that are 1, 2, 3, 5, 6, 10, 15, and 30. Therefore, the greatest common factor of 30 and 60 is 30.

GCF of 30 and 60 by Prime Factorization

Prime factorization of 30 and 60 is (2 × 3 × 5) and (2 × 2 × 3 × 5) respectively. As visible, 30 and 60 have common prime factors. Hence, the GCF of 30 and 60 is 2 × 3 × 5 = 30.

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GCF of 30 and 60 Examples

Example 1: The product of two numbers is 1800. If their GCF is 30, what is their LCM?

Solution:

Given: GCF = 30 and product of numbers = 1800
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1800/30
Therefore, the LCM is 60.
Example 2: Find the GCF of 30 and 60, if their LCM is 60.

Solution:

∵ LCM × GCF = 30 × 60
⇒ GCF(30, 60) = (30 × 60)/60 = 30
Therefore, the greatest common factor of 30 and 60 is 30.
Example 3: For two numbers, GCF = 30 and LCM = 60. If one number is 30, find the other number.

Solution:

Given: GCF (y, 30) = 30 and LCM (y, 30) = 60
∵ GCF × LCM = 30 × (y)
⇒ y = (GCF × LCM)/30
⇒ y = (30 × 60)/30
⇒ y = 60
Therefore, the other number is 60.

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FAQs on GCF of 30 and 60

What is the GCF of 30 and 60?

The GCF of 30 and 60 is 30. To calculate the GCF (Greatest Common Factor) of 30 and 60, we need to factor each number (factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30; factors of 60 = 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60) and choose the greatest factor that exactly divides both 30 and 60, i.e., 30.

What is the Relation Between LCM and GCF of 30, 60?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 30 and 60, i.e. GCF × LCM = 30 × 60.

How to Find the GCF of 30 and 60 by Prime Factorization?

To find the GCF of 30 and 60, we will find the prime factorization of the given numbers, i.e. 30 = 2 × 3 × 5; 60 = 2 × 2 × 3 × 5.
⇒ Since 2, 3, 5 are common terms in the prime factorization of 30 and 60. Hence, GCF(30, 60) = 2 × 3 × 5 = 30
☛ Prime Numbers

How to Find the GCF of 30 and 60 by Long Division Method?

To find the GCF of 30, 60 using long division method, 60 is divided by 30. The corresponding divisor (30) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 30 and 60?

There are three commonly used methods to find the GCF of 30 and 60.

By Long Division
By Listing Common Factors
By Prime Factorization

If the GCF of 60 and 30 is 30, Find its LCM.

GCF(60, 30) × LCM(60, 30) = 60 × 30
Since the GCF of 60 and 30 = 30
⇒ 30 × LCM(60, 30) = 1800
Therefore, LCM = 60
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