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GCF of 15 and 18

GCF of 15 and 18 is the largest possible number that divides 15 and 18 exactly without any remainder. The factors of 15 and 18 are 1, 3, 5, 15 and 1, 2, 3, 6, 9, 18 respectively. There are 3 commonly used methods to find the GCF of 15 and 18 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 15 and 18
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 18?

Answer: GCF of 15 and 18 is 3.

Explanation:

The GCF of two non-zero integers, x(15) and y(18), is the greatest positive integer m(3) that divides both x(15) and y(18) without any remainder.

Methods to Find GCF of 15 and 18

The methods to find the GCF of 15 and 18 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 15 and 18 by Long Division

GCF of 15 and 18 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 18 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 15 and 18.

GCF of 15 and 18 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 18: 1, 2, 3, 6, 9, 18

There are 2 common factors of 15 and 18, that are 1 and 3. Therefore, the greatest common factor of 15 and 18 is 3.

GCF of 15 and 18 by Prime Factorization

Prime factorization of 15 and 18 is (3 × 5) and (2 × 3 × 3) respectively. As visible, 15 and 18 have only one common prime factor i.e. 3. Hence, the GCF of 15 and 18 is 3.

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GCF of 15 and 18 Examples

Example 1: Find the GCF of 15 and 18, if their LCM is 90.

Solution:

∵ LCM × GCF = 15 × 18
⇒ GCF(15, 18) = (15 × 18)/90 = 3
Therefore, the greatest common factor of 15 and 18 is 3.
Example 2: The product of two numbers is 270. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 270
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 270/3
Therefore, the LCM is 90.
Example 3: Find the greatest number that divides 15 and 18 exactly.

Solution:

The greatest number that divides 15 and 18 exactly is their greatest common factor, i.e. GCF of 15 and 18.
⇒ Factors of 15 and 18:
- Factors of 15 = 1, 3, 5, 15
- Factors of 18 = 1, 2, 3, 6, 9, 18
Therefore, the GCF of 15 and 18 is 3.

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FAQs on GCF of 15 and 18

What is the GCF of 15 and 18?

The GCF of 15 and 18 is 3. To calculate the greatest common factor (GCF) of 15 and 18, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 18 = 1, 2, 3, 6, 9, 18) and choose the greatest factor that exactly divides both 15 and 18, i.e., 3.

What are the Methods to Find GCF of 15 and 18?

There are three commonly used methods to find the GCF of 15 and 18.

By Euclidean Algorithm
By Prime Factorization
By Long Division

If the GCF of 18 and 15 is 3, Find its LCM.

GCF(18, 15) × LCM(18, 15) = 18 × 15
Since the GCF of 18 and 15 = 3
⇒ 3 × LCM(18, 15) = 270
Therefore, LCM = 90
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 15, 18?

The following equation can be used to express the relation between LCM and GCF of 15 and 18, i.e. GCF × LCM = 15 × 18.

How to Find the GCF of 15 and 18 by Prime Factorization?

To find the GCF of 15 and 18, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 18 = 2 × 3 × 3.
⇒ Since 3 is the only common prime factor of 15 and 18. Hence, GCF (15, 18) = 3.
☛ What are Prime Numbers?

How to Find the GCF of 15 and 18 by Long Division Method?

To find the GCF of 15, 18 using long division method, 18 is divided by 15. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

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