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GCF of 12 and 15

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

1.	GCF of 12 and 15
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 12 and 15?

Answer: GCF of 12 and 15 is 3.

Explanation:

The GCF of two non-zero integers, x(12) and y(15), is the greatest positive integer m(3) that divides both x(12) and y(15) without any remainder.

Methods to Find GCF of 12 and 15

Let's look at the different methods for finding the GCF of 12 and 15.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 12 and 15 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 = 15 and Y = 12

GCF(15, 12) = GCF(12, 15 mod 12) = GCF(12, 3)
GCF(12, 3) = GCF(3, 12 mod 3) = GCF(3, 0)
GCF(3, 0) = 3 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 12 and 15 is 3.

GCF of 12 and 15 by Long Division

GCF of 12 and 15 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 15 (larger number) by 12 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (12) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 12 and 15.

GCF of 12 and 15 by Prime Factorization

Prime factorization of 12 and 15 is (2 × 2 × 3) and (3 × 5) respectively. As visible, 12 and 15 have only one common prime factor i.e. 3. Hence, the GCF of 12 and 15 is 3.

☛ Also Check:

GCF of 12 and 15 Examples

Example 1: Find the greatest number that divides 12 and 15 exactly.

Solution:

The greatest number that divides 12 and 15 exactly is their greatest common factor, i.e. GCF of 12 and 15.
⇒ Factors of 12 and 15:
- Factors of 12 = 1, 2, 3, 4, 6, 12
- Factors of 15 = 1, 3, 5, 15
Therefore, the GCF of 12 and 15 is 3.
Example 2: The product of two numbers is 180. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 180
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 180/3
Therefore, the LCM is 60.
Example 3: Find the GCF of 12 and 15, if their LCM is 60.

Solution:

∵ LCM × GCF = 12 × 15
⇒ GCF(12, 15) = (12 × 15)/60 = 3
Therefore, the greatest common factor of 12 and 15 is 3.

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FAQs on GCF of 12 and 15

What is the GCF of 12 and 15?

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

How to Find the GCF of 12 and 15 by Prime Factorization?

To find the GCF of 12 and 15, we will find the prime factorization of the given numbers, i.e. 12 = 2 × 2 × 3; 15 = 3 × 5.
⇒ Since 3 is the only common prime factor of 12 and 15. Hence, GCF (12, 15) = 3.
☛ Prime Numbers

If the GCF of 15 and 12 is 3, Find its LCM.

GCF(15, 12) × LCM(15, 12) = 15 × 12
Since the GCF of 15 and 12 = 3
⇒ 3 × LCM(15, 12) = 180
Therefore, LCM = 60
☛ GCF Calculator

What are the Methods to Find GCF of 12 and 15?

There are three commonly used methods to find the GCF of 12 and 15.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 12 and 15 by Long Division Method?

To find the GCF of 12, 15 using long division method, 15 is divided by 12. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 12, 15?

The following equation can be used to express the relation between LCM and GCF of 12 and 15, i.e. GCF × LCM = 12 × 15.

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