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GCF of 15 and 16

GCF of 15 and 16 is the largest possible number that divides 15 and 16 exactly without any remainder. The factors of 15 and 16 are 1, 3, 5, 15 and 1, 2, 4, 8, 16 respectively. There are 3 commonly used methods to find the GCF of 15 and 16 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 15 and 16
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 15 and 16?

Answer: GCF of 15 and 16 is 1.

Explanation:

The GCF of two non-zero integers, x(15) and y(16), is the greatest positive integer m(1) that divides both x(15) and y(16) without any remainder.

Methods to Find GCF of 15 and 16

The methods to find the GCF of 15 and 16 are explained below.

Long Division Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 15 and 16 by Long Division

GCF of 15 and 16 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 16 (larger number) by 15 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (15) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 15 and 16.

GCF of 15 and 16 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 = 16 and Y = 15

GCF(16, 15) = GCF(15, 16 mod 15) = GCF(15, 1)
GCF(15, 1) = GCF(1, 15 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 15 and 16 is 1.

GCF of 15 and 16 by Listing Common Factors

Factors of 15: 1, 3, 5, 15
Factors of 16: 1, 2, 4, 8, 16

Since, 1 is the only common factor between 15 and 16. The Greatest Common Factor of 15 and 16 is 1.

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GCF of 15 and 16 Examples

Example 1: Find the greatest number that divides 15 and 16 exactly.

Solution:

The greatest number that divides 15 and 16 exactly is their greatest common factor, i.e. GCF of 15 and 16.
⇒ Factors of 15 and 16:
- Factors of 15 = 1, 3, 5, 15
- Factors of 16 = 1, 2, 4, 8, 16
Therefore, the GCF of 15 and 16 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 240. If one number is 15, find the other number.

Solution:

Given: GCF (y, 15) = 1 and LCM (y, 15) = 240
∵ GCF × LCM = 15 × (y)
⇒ y = (GCF × LCM)/15
⇒ y = (1 × 240)/15
⇒ y = 16
Therefore, the other number is 16.
Example 3: Find the GCF of 15 and 16, if their LCM is 240.

Solution:

∵ LCM × GCF = 15 × 16
⇒ GCF(15, 16) = (15 × 16)/240 = 1
Therefore, the greatest common factor of 15 and 16 is 1.

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FAQs on GCF of 15 and 16

What is the GCF of 15 and 16?

The GCF of 15 and 16 is 1. To calculate the greatest common factor (GCF) of 15 and 16, we need to factor each number (factors of 15 = 1, 3, 5, 15; factors of 16 = 1, 2, 4, 8, 16) and choose the greatest factor that exactly divides both 15 and 16, i.e., 1.

What are the Methods to Find GCF of 15 and 16?

There are three commonly used methods to find the GCF of 15 and 16.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 15 and 16 by Long Division Method?

To find the GCF of 15, 16 using long division method, 16 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, 16?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 15 and 16, i.e. GCF × LCM = 15 × 16.

If the GCF of 16 and 15 is 1, Find its LCM.

GCF(16, 15) × LCM(16, 15) = 16 × 15
Since the GCF of 16 and 15 = 1
⇒ 1 × LCM(16, 15) = 240
Therefore, LCM = 240
☛ Greatest Common Factor Calculator

How to Find the GCF of 15 and 16 by Prime Factorization?

To find the GCF of 15 and 16, we will find the prime factorization of the given numbers, i.e. 15 = 3 × 5; 16 = 2 × 2 × 2 × 2.
⇒ There is no common prime factor for 15 and 16. Hence, GCF (15, 16) = 1.
☛ What are Prime Numbers?

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