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GCF of 15 and 28

GCF of 15 and 28 is the largest possible number that divides 15 and 28 exactly without any remainder. The factors of 15 and 28 are 1, 3, 5, 15 and 1, 2, 4, 7, 14, 28 respectively. There are 3 commonly used methods to find the GCF of 15 and 28 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 15 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 28?

Answer: GCF of 15 and 28 is 1.

Explanation:

The GCF of two non-zero integers, x(15) and y(28), is the greatest positive integer m(1) that divides both x(15) and y(28) without any remainder.

Methods to Find GCF of 15 and 28

The methods to find the GCF of 15 and 28 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 15 and 28 by Long Division

GCF of 15 and 28 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 28 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (13).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 15 and 28.

GCF of 15 and 28 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 28: 1, 2, 4, 7, 14, 28

Since, 1 is the only common factor between 15 and 28. The Greatest Common Factor of 15 and 28 is 1.

GCF of 15 and 28 by Prime Factorization

Prime factorization of 15 and 28 is (3 × 5) and (2 × 2 × 7) respectively. As visible, there are no common prime factors between 15 and 28, i.e. they are co-prime. Hence, the GCF of 15 and 28 will be 1.

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GCF of 15 and 28 Examples

Example 1: Find the GCF of 15 and 28, if their LCM is 420.

Solution:

∵ LCM × GCF = 15 × 28
⇒ GCF(15, 28) = (15 × 28)/420 = 1
Therefore, the greatest common factor of 15 and 28 is 1.
Example 2: The product of two numbers is 420. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 420
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 420/1
Therefore, the LCM is 420.
Example 3: Find the greatest number that divides 15 and 28 exactly.

Solution:

The greatest number that divides 15 and 28 exactly is their greatest common factor, i.e. GCF of 15 and 28.
⇒ Factors of 15 and 28:
- Factors of 15 = 1, 3, 5, 15
- Factors of 28 = 1, 2, 4, 7, 14, 28
Therefore, the GCF of 15 and 28 is 1.

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FAQs on GCF of 15 and 28

What is the GCF of 15 and 28?

The GCF of 15 and 28 is 1. To calculate the GCF (Greatest Common Factor) of 15 and 28, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 15 and 28, i.e., 1.

How to Find the GCF of 15 and 28 by Prime Factorization?

To find the GCF of 15 and 28, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 28 = 2 × 2 × 7.
⇒ There is no common prime factor for 15 and 28. Hence, GCF (15, 28) = 1.
☛ Prime Numbers

How to Find the GCF of 15 and 28 by Long Division Method?

To find the GCF of 15, 28 using long division method, 28 is divided by 15. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 15, 28?

The following equation can be used to express the relation between LCM and GCF of 15 and 28, i.e. GCF × LCM = 15 × 28.

If the GCF of 28 and 15 is 1, Find its LCM.

GCF(28, 15) × LCM(28, 15) = 28 × 15
Since the GCF of 28 and 15 = 1
⇒ 1 × LCM(28, 15) = 420
Therefore, LCM = 420
☛ GCF Calculator

What are the Methods to Find GCF of 15 and 28?

There are three commonly used methods to find the GCF of 15 and 28.

By Euclidean Algorithm
By Prime Factorization
By Long Division

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