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GCF of 3 and 15

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

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

What is GCF of 3 and 15?

Answer: GCF of 3 and 15 is 3.

Explanation:

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

Methods to Find GCF of 3 and 15

Let's look at the different methods for finding the GCF of 3 and 15.

Long Division Method
Using Euclid's Algorithm
Prime Factorization Method

GCF of 3 and 15 by Long Division

GCF of 3 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 3 (smaller number).
Step 2: Since the remainder = 0, the divisor (3) is the GCF of 3 and 15.

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

GCF of 3 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 = 3

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

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

GCF of 3 and 15 by Prime Factorization

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

☛ Also Check:

GCF of 3 and 15 Examples

Example 1: Find the GCF of 3 and 15, if their LCM is 15.

Solution:

∵ LCM × GCF = 3 × 15
⇒ GCF(3, 15) = (3 × 15)/15 = 3
Therefore, the greatest common factor of 3 and 15 is 3.
Example 2: Find the greatest number that divides 3 and 15 exactly.

Solution:

The greatest number that divides 3 and 15 exactly is their greatest common factor, i.e. GCF of 3 and 15.
⇒ Factors of 3 and 15:
- Factors of 3 = 1, 3
- Factors of 15 = 1, 3, 5, 15
Therefore, the GCF of 3 and 15 is 3.
Example 3: For two numbers, GCF = 3 and LCM = 15. If one number is 3, find the other number.

Solution:

Given: GCF (x, 3) = 3 and LCM (x, 3) = 15
∵ GCF × LCM = 3 × (x)
⇒ x = (GCF × LCM)/3
⇒ x = (3 × 15)/3
⇒ x = 15
Therefore, the other number is 15.

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FAQs on GCF of 3 and 15

What is the GCF of 3 and 15?

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

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

GCF(15, 3) × LCM(15, 3) = 15 × 3
Since the GCF of 15 and 3 = 3
⇒ 3 × LCM(15, 3) = 45
Therefore, LCM = 15
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 3, 15?

The following equation can be used to express the relation between LCM and GCF of 3 and 15, i.e. GCF × LCM = 3 × 15.

How to Find the GCF of 3 and 15 by Prime Factorization?

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

How to Find the GCF of 3 and 15 by Long Division Method?

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

What are the Methods to Find GCF of 3 and 15?

There are three commonly used methods to find the GCF of 3 and 15.

By Listing Common Factors
By Long Division
By Prime Factorization

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