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GCF of 14 and 45

GCF of 14 and 45 is the largest possible number that divides 14 and 45 exactly without any remainder. The factors of 14 and 45 are 1, 2, 7, 14 and 1, 3, 5, 9, 15, 45 respectively. There are 3 commonly used methods to find the GCF of 14 and 45 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 14 and 45
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 45?

Answer: GCF of 14 and 45 is 1.

Explanation:

The GCF of two non-zero integers, x(14) and y(45), is the greatest positive integer m(1) that divides both x(14) and y(45) without any remainder.

Methods to Find GCF of 14 and 45

The methods to find the GCF of 14 and 45 are explained below.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 14 and 45 by Prime Factorization

Prime factorization of 14 and 45 is (2 × 7) and (3 × 3 × 5) respectively. As visible, there are no common prime factors between 14 and 45, i.e. they are co-prime. Hence, the GCF of 14 and 45 will be 1.

GCF of 14 and 45 by Long Division

GCF of 14 and 45 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 45 (larger number) by 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (3).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 14 and 45.

GCF of 14 and 45 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 = 45 and Y = 14

GCF(45, 14) = GCF(14, 45 mod 14) = GCF(14, 3)
GCF(14, 3) = GCF(3, 14 mod 3) = GCF(3, 2)
GCF(3, 2) = GCF(2, 3 mod 2) = GCF(2, 1)
GCF(2, 1) = 1 (∵ GCF(X, 1) = 1)

Therefore, the value of GCF of 14 and 45 is 1.

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GCF of 14 and 45 Examples

Example 1: For two numbers, GCF = 1 and LCM = 630. If one number is 45, find the other number.

Solution:

Given: GCF (y, 45) = 1 and LCM (y, 45) = 630
∵ GCF × LCM = 45 × (y)
⇒ y = (GCF × LCM)/45
⇒ y = (1 × 630)/45
⇒ y = 14
Therefore, the other number is 14.
Example 2: Find the GCF of 14 and 45, if their LCM is 630.

Solution:

∵ LCM × GCF = 14 × 45
⇒ GCF(14, 45) = (14 × 45)/630 = 1
Therefore, the greatest common factor of 14 and 45 is 1.
Example 3: The product of two numbers is 630. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 630
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 630/1
Therefore, the LCM is 630.

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FAQs on GCF of 14 and 45

What is the GCF of 14 and 45?

The GCF of 14 and 45 is 1. To calculate the GCF of 14 and 45, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 45 = 1, 3, 5, 9, 15, 45) and choose the greatest factor that exactly divides both 14 and 45, i.e., 1.

How to Find the GCF of 14 and 45 by Long Division Method?

To find the GCF of 14, 45 using long division method, 45 is divided by 14. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

If the GCF of 45 and 14 is 1, Find its LCM.

GCF(45, 14) × LCM(45, 14) = 45 × 14
Since the GCF of 45 and 14 = 1
⇒ 1 × LCM(45, 14) = 630
Therefore, LCM = 630
☛ Greatest Common Factor Calculator

What are the Methods to Find GCF of 14 and 45?

There are three commonly used methods to find the GCF of 14 and 45.

By Euclidean Algorithm
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 14, 45?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 14 and 45, i.e. GCF × LCM = 14 × 45.

How to Find the GCF of 14 and 45 by Prime Factorization?

To find the GCF of 14 and 45, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 45 = 3 × 3 × 5.
⇒ There is no common prime factor for 14 and 45. Hence, GCF (14, 45) = 1.
☛ What are Prime Numbers?

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