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GCF of 15 and 45

GCF of 15 and 45 is the largest possible number that divides 15 and 45 exactly without any remainder. The factors of 15 and 45 are 1, 3, 5, 15 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used methods to find the GCF of 15 and 45 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 15 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 45?

Answer: GCF of 15 and 45 is 15.

Explanation:

The GCF of two non-zero integers, x(15) and y(45), is the greatest positive integer m(15) that divides both x(15) and y(45) without any remainder.

Methods to Find GCF of 15 and 45

The methods to find the GCF of 15 and 45 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 15 and 45 by Prime Factorization

Prime factorization of 15 and 45 is (3 × 5) and (3 × 3 × 5) respectively. As visible, 15 and 45 have common prime factors. Hence, the GCF of 15 and 45 is 3 × 5 = 15.

GCF of 15 and 45 by Long Division

GCF of 15 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 15 (smaller number).
Step 2: Since the remainder = 0, the divisor (15) is the GCF of 15 and 45.

The corresponding divisor (15) is the GCF of 15 and 45.

GCF of 15 and 45 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 = 45 and Y = 15

GCF(45, 15) = GCF(15, 45 mod 15) = GCF(15, 0)
GCF(15, 0) = 15 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 15 and 45 is 15.

☛ Also Check:

GCF of 15 and 45 Examples

Example 1: Find the GCF of 15 and 45, if their LCM is 45.

Solution:

∵ LCM × GCF = 15 × 45
⇒ GCF(15, 45) = (15 × 45)/45 = 15
Therefore, the greatest common factor of 15 and 45 is 15.
Example 2: Find the greatest number that divides 15 and 45 exactly.

Solution:

The greatest number that divides 15 and 45 exactly is their greatest common factor, i.e. GCF of 15 and 45.
⇒ Factors of 15 and 45:
- Factors of 15 = 1, 3, 5, 15
- Factors of 45 = 1, 3, 5, 9, 15, 45
Therefore, the GCF of 15 and 45 is 15.
Example 3: For two numbers, GCF = 15 and LCM = 45. If one number is 45, find the other number.

Solution:

Given: GCF (z, 45) = 15 and LCM (z, 45) = 45
∵ GCF × LCM = 45 × (z)
⇒ z = (GCF × LCM)/45
⇒ z = (15 × 45)/45
⇒ z = 15
Therefore, the other number is 15.

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FAQs on GCF of 15 and 45

What is the GCF of 15 and 45?

The GCF of 15 and 45 is 15. To calculate the GCF of 15 and 45, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 15 and 45, i.e., 15.

If the GCF of 45 and 15 is 15, Find its LCM.

GCF(45, 15) × LCM(45, 15) = 45 × 15
Since the GCF of 45 and 15 = 15
⇒ 15 × LCM(45, 15) = 675
Therefore, LCM = 45
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 15, 45?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 15 and 45, i.e. GCF × LCM = 15 × 45.

How to Find the GCF of 15 and 45 by Prime Factorization?

To find the GCF of 15 and 45, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 45 = 3 × 3 × 5.
⇒ Since 3, 5 are common terms in the prime factorization of 15 and 45. Hence, GCF(15, 45) = 3 × 5 = 15
☛ Prime Numbers

What are the Methods to Find GCF of 15 and 45?

There are three commonly used methods to find the GCF of 15 and 45.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the GCF of 15 and 45 by Long Division Method?

To find the GCF of 15, 45 using long division method, 45 is divided by 15. The corresponding divisor (15) when remainder equals 0 is taken as GCF.

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