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GCF of 15 and 36

GCF of 15 and 36 is the largest possible number that divides 15 and 36 exactly without any remainder. The factors of 15 and 36 are 1, 3, 5, 15 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 15 and 36 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 15 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 36?

Answer: GCF of 15 and 36 is 3.

Explanation:

The GCF of two non-zero integers, x(15) and y(36), is the greatest positive integer m(3) that divides both x(15) and y(36) without any remainder.

Methods to Find GCF of 15 and 36

The methods to find the GCF of 15 and 36 are explained below.

Long Division Method
Prime Factorization Method
Listing Common Factors

GCF of 15 and 36 by Long Division

GCF of 15 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (6).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (3) is the GCF of 15 and 36.

GCF of 15 and 36 by Prime Factorization

Prime factorization of 15 and 36 is (3 × 5) and (2 × 2 × 3 × 3) respectively. As visible, 15 and 36 have only one common prime factor i.e. 3. Hence, the GCF of 15 and 36 is 3.

GCF of 15 and 36 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 2 common factors of 15 and 36, that are 1 and 3. Therefore, the greatest common factor of 15 and 36 is 3.

☛ Also Check:

GCF of 15 and 36 Examples

Example 1: Find the greatest number that divides 15 and 36 exactly.

Solution:

The greatest number that divides 15 and 36 exactly is their greatest common factor, i.e. GCF of 15 and 36.
⇒ Factors of 15 and 36:
- Factors of 15 = 1, 3, 5, 15
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the GCF of 15 and 36 is 3.
Example 2: Find the GCF of 15 and 36, if their LCM is 180.

Solution:

∵ LCM × GCF = 15 × 36
⇒ GCF(15, 36) = (15 × 36)/180 = 3
Therefore, the greatest common factor of 15 and 36 is 3.
Example 3: The product of two numbers is 540. If their GCF is 3, what is their LCM?

Solution:

Given: GCF = 3 and product of numbers = 540
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 540/3
Therefore, the LCM is 180.

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FAQs on GCF of 15 and 36

What is the GCF of 15 and 36?

The GCF of 15 and 36 is 3. To calculate the GCF (Greatest Common Factor) of 15 and 36, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 15 and 36, i.e., 3.

What is the Relation Between LCM and GCF of 15, 36?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 15 and 36, i.e. GCF × LCM = 15 × 36.

How to Find the GCF of 15 and 36 by Long Division Method?

To find the GCF of 15, 36 using long division method, 36 is divided by 15. The corresponding divisor (3) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 15 and 36?

There are three commonly used methods to find the GCF of 15 and 36.

By Euclidean Algorithm
By Long Division
By Prime Factorization

How to Find the GCF of 15 and 36 by Prime Factorization?

To find the GCF of 15 and 36, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 36 = 2 × 2 × 3 × 3.
⇒ Since 3 is the only common prime factor of 15 and 36. Hence, GCF (15, 36) = 3.
☛ What is a Prime Number?

If the GCF of 36 and 15 is 3, Find its LCM.

GCF(36, 15) × LCM(36, 15) = 36 × 15
Since the GCF of 36 and 15 = 3
⇒ 3 × LCM(36, 15) = 540
Therefore, LCM = 180
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