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GCF of 12 and 30

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

1.	GCF of 12 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 30?

Answer: GCF of 12 and 30 is 6.

Explanation:

The GCF of two non-zero integers, x(12) and y(30), is the greatest positive integer m(6) that divides both x(12) and y(30) without any remainder.

Methods to Find GCF of 12 and 30

Let's look at the different methods for finding the GCF of 12 and 30.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 12 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 = 12

GCF(30, 12) = GCF(12, 30 mod 12) = GCF(12, 6)
GCF(12, 6) = GCF(6, 12 mod 6) = GCF(6, 0)
GCF(6, 0) = 6 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 30 is 6.

GCF of 12 and 30 by Long Division

GCF of 12 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 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (6) is the GCF of 12 and 30.

GCF of 12 and 30 by Listing Common Factors

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

There are 4 common factors of 12 and 30, that are 1, 2, 3, and 6. Therefore, the greatest common factor of 12 and 30 is 6.

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GCF of 12 and 30 Examples

Example 1: The product of two numbers is 360. If their GCF is 6, what is their LCM?

Solution:

Given: GCF = 6 and product of numbers = 360
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 360/6
Therefore, the LCM is 60.
Example 2: Find the greatest number that divides 12 and 30 exactly.

Solution:

The greatest number that divides 12 and 30 exactly is their greatest common factor, i.e. GCF of 12 and 30.
⇒ Factors of 12 and 30:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 12 and 30 is 6.
Example 3: Find the GCF of 12 and 30, if their LCM is 60.

Solution:

∵ LCM × GCF = 12 × 30
⇒ GCF(12, 30) = (12 × 30)/60 = 6
Therefore, the greatest common factor of 12 and 30 is 6.

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FAQs on GCF of 12 and 30

What is the GCF of 12 and 30?

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

What is the Relation Between LCM and GCF of 12, 30?

The following equation can be used to express the relation between LCM and GCF of 12 and 30, i.e. GCF × LCM = 12 × 30.

How to Find the GCF of 12 and 30 by Long Division Method?

To find the GCF of 12, 30 using long division method, 30 is divided by 12. The corresponding divisor (6) when remainder equals 0 is taken as GCF.

How to Find the GCF of 12 and 30 by Prime Factorization?

To find the GCF of 12 and 30, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 30 = 2 × 3 × 5.
⇒ Since 2, 3 are common terms in the prime factorization of 12 and 30. Hence, GCF(12, 30) = 2 × 3 = 6
☛ What is a Prime Number?

What are the Methods to Find GCF of 12 and 30?

There are three commonly used methods to find the GCF of 12 and 30.

By Listing Common Factors
By Prime Factorization
By Long Division

If the GCF of 30 and 12 is 6, Find its LCM.

GCF(30, 12) × LCM(30, 12) = 30 × 12
Since the GCF of 30 and 12 = 6
⇒ 6 × LCM(30, 12) = 360
Therefore, LCM = 60
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