A day full of math games & activities. Find one near you.

GCF of 13 and 15

GCF of 13 and 15 is the largest possible number that divides 13 and 15 exactly without any remainder. The factors of 13 and 15 are 1, 13 and 1, 3, 5, 15 respectively. There are 3 commonly used methods to find the GCF of 13 and 15 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 13 and 15
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 13 and 15?

Answer: GCF of 13 and 15 is 1.

Explanation:

The GCF of two non-zero integers, x(13) and y(15), is the greatest positive integer m(1) that divides both x(13) and y(15) without any remainder.

Methods to Find GCF of 13 and 15

Let's look at the different methods for finding the GCF of 13 and 15.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 13 and 15 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 = 15 and Y = 13

GCF(15, 13) = GCF(13, 15 mod 13) = GCF(13, 2)
GCF(13, 2) = GCF(2, 13 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 13 and 15 is 1.

GCF of 13 and 15 by Long Division

GCF of 13 and 15 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

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

The corresponding divisor (1) is the GCF of 13 and 15.

GCF of 13 and 15 by Listing Common Factors

Factors of 13: 1, 13
Factors of 15: 1, 3, 5, 15

Since, 1 is the only common factor between 13 and 15. The Greatest Common Factor of 13 and 15 is 1.

☛ Also Check:

GCF of 13 and 15 Examples

Example 1: The product of two numbers is 195. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 195
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 195/1
Therefore, the LCM is 195.
Example 2: Find the greatest number that divides 13 and 15 exactly.

Solution:

The greatest number that divides 13 and 15 exactly is their greatest common factor, i.e. GCF of 13 and 15.
⇒ Factors of 13 and 15:
- Factors of 13 = 1, 13
- Factors of 15 = 1, 3, 5, 15
Therefore, the GCF of 13 and 15 is 1.
Example 3: Find the GCF of 13 and 15, if their LCM is 195.

Solution:

∵ LCM × GCF = 13 × 15
⇒ GCF(13, 15) = (13 × 15)/195 = 1
Therefore, the greatest common factor of 13 and 15 is 1.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 13 and 15

What is the GCF of 13 and 15?

The GCF of 13 and 15 is 1. To calculate the greatest common factor of 13 and 15, we need to factor each number (factors of 13 = 1, 13; factors of 15 = 1, 3, 5, 15) and choose the greatest factor that exactly divides both 13 and 15, i.e., 1.

What are the Methods to Find GCF of 13 and 15?

There are three commonly used methods to find the GCF of 13 and 15.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 13 and 15 by Long Division Method?

To find the GCF of 13, 15 using long division method, 15 is divided by 13. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 13 and 15 by Prime Factorization?

To find the GCF of 13 and 15, we will find the prime factorization of the given numbers, i.e. 13 = 13; 15 = 3 × 5.
⇒ There is no common prime factor for 13 and 15. Hence, GCF (13, 15) = 1.
☛ Prime Numbers

If the GCF of 15 and 13 is 1, Find its LCM.

GCF(15, 13) × LCM(15, 13) = 15 × 13
Since the GCF of 15 and 13 = 1
⇒ 1 × LCM(15, 13) = 195
Therefore, LCM = 195
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 13, 15?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 13 and 15, i.e. GCF × LCM = 13 × 15.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum