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GCF of 15 and 20

GCF of 15 and 20 is the largest possible number that divides 15 and 20 exactly without any remainder. The factors of 15 and 20 are 1, 3, 5, 15 and 1, 2, 4, 5, 10, 20 respectively. There are 3 commonly used methods to find the GCF of 15 and 20 - prime factorization, long division, and Euclidean algorithm.

1.	GCF of 15 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 20?

Answer: GCF of 15 and 20 is 5.

Explanation:

The GCF of two non-zero integers, x(15) and y(20), is the greatest positive integer m(5) that divides both x(15) and y(20) without any remainder.

Methods to Find GCF of 15 and 20

The methods to find the GCF of 15 and 20 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 15 and 20 by Prime Factorization

Prime factorization of 15 and 20 is (3 × 5) and (2 × 2 × 5) respectively. As visible, 15 and 20 have only one common prime factor i.e. 5. Hence, the GCF of 15 and 20 is 5.

GCF of 15 and 20 by Long Division

GCF of 15 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 20 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (5) is the GCF of 15 and 20.

GCF of 15 and 20 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 20: 1, 2, 4, 5, 10, 20

There are 2 common factors of 15 and 20, that are 1 and 5. Therefore, the greatest common factor of 15 and 20 is 5.

☛ Also Check:

GCF of 15 and 20 Examples

Example 1: Find the greatest number that divides 15 and 20 exactly.

Solution:

The greatest number that divides 15 and 20 exactly is their greatest common factor, i.e. GCF of 15 and 20.
⇒ Factors of 15 and 20:
- Factors of 15 = 1, 3, 5, 15
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 15 and 20 is 5.
Example 2: Find the GCF of 15 and 20, if their LCM is 60.

Solution:

∵ LCM × GCF = 15 × 20
⇒ GCF(15, 20) = (15 × 20)/60 = 5
Therefore, the greatest common factor of 15 and 20 is 5.
Example 3: For two numbers, GCF = 5 and LCM = 60. If one number is 20, find the other number.

Solution:

Given: GCF (z, 20) = 5 and LCM (z, 20) = 60
∵ GCF × LCM = 20 × (z)
⇒ z = (GCF × LCM)/20
⇒ z = (5 × 60)/20
⇒ z = 15
Therefore, the other number is 15.

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FAQs on GCF of 15 and 20

What is the GCF of 15 and 20?

The GCF of 15 and 20 is 5. To calculate the GCF (Greatest Common Factor) of 15 and 20, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 20 = 1, 2, 4, 5, 10, 20) and choose the greatest factor that exactly divides both 15 and 20, i.e., 5.

How to Find the GCF of 15 and 20 by Prime Factorization?

To find the GCF of 15 and 20, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 20 = 2 × 2 × 5.
⇒ Since 5 is the only common prime factor of 15 and 20. Hence, GCF (15, 20) = 5.
☛ Prime Numbers

How to Find the GCF of 15 and 20 by Long Division Method?

To find the GCF of 15, 20 using long division method, 20 is divided by 15. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 15 and 20?

There are three commonly used methods to find the GCF of 15 and 20.

By Euclidean Algorithm
By Prime Factorization
By Long Division

If the GCF of 20 and 15 is 5, Find its LCM.

GCF(20, 15) × LCM(20, 15) = 20 × 15
Since the GCF of 20 and 15 = 5
⇒ 5 × LCM(20, 15) = 300
Therefore, LCM = 60
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 15, 20?

The following equation can be used to express the relation between LCM and GCF of 15 and 20, i.e. GCF × LCM = 15 × 20.

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