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GCF of 9 and 14

GCF of 9 and 14 is the largest possible number that divides 9 and 14 exactly without any remainder. The factors of 9 and 14 are 1, 3, 9 and 1, 2, 7, 14 respectively. There are 3 commonly used methods to find the GCF of 9 and 14 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 9 and 14
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 9 and 14?

Answer: GCF of 9 and 14 is 1.

Explanation:

The GCF of two non-zero integers, x(9) and y(14), is the greatest positive integer m(1) that divides both x(9) and y(14) without any remainder.

Methods to Find GCF of 9 and 14

The methods to find the GCF of 9 and 14 are explained below.

Using Euclid's Algorithm
Long Division Method
Listing Common Factors

GCF of 9 and 14 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 = 14 and Y = 9

GCF(14, 9) = GCF(9, 14 mod 9) = GCF(9, 5)
GCF(9, 5) = GCF(5, 9 mod 5) = GCF(5, 4)
GCF(5, 4) = GCF(4, 5 mod 4) = GCF(4, 1)
GCF(4, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 9 and 14 is 1.

GCF of 9 and 14 by Long Division

GCF of 9 and 14 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 14 (larger number) by 9 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (9) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 9 and 14.

GCF of 9 and 14 by Listing Common Factors

Factors of 9: 1, 3, 9
Factors of 14: 1, 2, 7, 14

Since, 1 is the only common factor between 9 and 14. The Greatest Common Factor of 9 and 14 is 1.

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GCF of 9 and 14 Examples

Example 1: For two numbers, GCF = 1 and LCM = 126. If one number is 9, find the other number.

Solution:

Given: GCF (x, 9) = 1 and LCM (x, 9) = 126
∵ GCF × LCM = 9 × (x)
⇒ x = (GCF × LCM)/9
⇒ x = (1 × 126)/9
⇒ x = 14
Therefore, the other number is 14.
Example 2: Find the GCF of 9 and 14, if their LCM is 126.

Solution:

∵ LCM × GCF = 9 × 14
⇒ GCF(9, 14) = (9 × 14)/126 = 1
Therefore, the greatest common factor of 9 and 14 is 1.
Example 3: Find the greatest number that divides 9 and 14 exactly.

Solution:

The greatest number that divides 9 and 14 exactly is their greatest common factor, i.e. GCF of 9 and 14.
⇒ Factors of 9 and 14:
- Factors of 9 = 1, 3, 9
- Factors of 14 = 1, 2, 7, 14
Therefore, the GCF of 9 and 14 is 1.

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FAQs on GCF of 9 and 14

What is the GCF of 9 and 14?

The GCF of 9 and 14 is 1. To calculate the greatest common factor (GCF) of 9 and 14, we need to factor each number (factors of 9 = 1, 3, 9; factors of 14 = 1, 2, 7, 14) and choose the greatest factor that exactly divides both 9 and 14, i.e., 1.

What are the Methods to Find GCF of 9 and 14?

There are three commonly used methods to find the GCF of 9 and 14.

By Prime Factorization
By Long Division
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 9, 14?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 9 and 14, i.e. GCF × LCM = 9 × 14.

If the GCF of 14 and 9 is 1, Find its LCM.

GCF(14, 9) × LCM(14, 9) = 14 × 9
Since the GCF of 14 and 9 = 1
⇒ 1 × LCM(14, 9) = 126
Therefore, LCM = 126
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How to Find the GCF of 9 and 14 by Long Division Method?

To find the GCF of 9, 14 using long division method, 14 is divided by 9. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 9 and 14 by Prime Factorization?

To find the GCF of 9 and 14, we will find the prime factorization of the given numbers, i.e. 9 = 3 × 3; 14 = 2 × 7.
⇒ There is no common prime factor for 9 and 14. Hence, GCF (9, 14) = 1.
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