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GCF of 14 and 15

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

1.	GCF of 14 and 15
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 15?

Answer: GCF of 14 and 15 is 1.

Explanation:

The GCF of two non-zero integers, x(14) and y(15), is the greatest positive integer m(1) that divides both x(14) and y(15) without any remainder.

Methods to Find GCF of 14 and 15

Let's look at the different methods for finding the GCF of 14 and 15.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 14 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 = 14

GCF(15, 14) = GCF(14, 15 mod 14) = GCF(14, 1)
GCF(14, 1) = GCF(1, 14 mod 1) = GCF(1, 0)
GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 14 and 15 is 1.

GCF of 14 and 15 by Prime Factorization

Prime factorization of 14 and 15 is (2 × 7) and (3 × 5) respectively. As visible, there are no common prime factors between 14 and 15, i.e. they are co-prime. Hence, the GCF of 14 and 15 will be 1.

GCF of 14 and 15 by Long Division

GCF of 14 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 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (1).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 14 and 15.

☛ Also Check:

GCF of 14 and 15 Examples

Example 1: For two numbers, GCF = 1 and LCM = 210. If one number is 14, find the other number.

Solution:

Given: GCF (z, 14) = 1 and LCM (z, 14) = 210
∵ GCF × LCM = 14 × (z)
⇒ z = (GCF × LCM)/14
⇒ z = (1 × 210)/14
⇒ z = 15
Therefore, the other number is 15.
Example 2: Find the GCF of 14 and 15, if their LCM is 210.

Solution:

∵ LCM × GCF = 14 × 15
⇒ GCF(14, 15) = (14 × 15)/210 = 1
Therefore, the greatest common factor of 14 and 15 is 1.
Example 3: The product of two numbers is 210. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 210
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 210/1
Therefore, the LCM is 210.

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FAQs on GCF of 14 and 15

What is the GCF of 14 and 15?

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

How to Find the GCF of 14 and 15 by Long Division Method?

To find the GCF of 14, 15 using long division method, 15 is divided by 14. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 14 and 15?

There are three commonly used methods to find the GCF of 14 and 15.

By Long Division
By Prime Factorization
By Listing Common Factors

How to Find the GCF of 14 and 15 by Prime Factorization?

To find the GCF of 14 and 15, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 15 = 3 × 5.
⇒ There is no common prime factor for 14 and 15. Hence, GCF (14, 15) = 1.
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 14, 15?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 14 and 15, i.e. GCF × LCM = 14 × 15.

If the GCF of 15 and 14 is 1, Find its LCM.

GCF(15, 14) × LCM(15, 14) = 15 × 14
Since the GCF of 15 and 14 = 1
⇒ 1 × LCM(15, 14) = 210
Therefore, LCM = 210
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