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GCF of 5 and 14

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

1.	GCF of 5 and 14
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 5 and 14?

Answer: GCF of 5 and 14 is 1.

Explanation:

The GCF of two non-zero integers, x(5) and y(14), is the greatest positive integer m(1) that divides both x(5) and y(14) without any remainder.

Methods to Find GCF of 5 and 14

The methods to find the GCF of 5 and 14 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 5 and 14 by Listing Common Factors

Factors of 5: 1, 5
Factors of 14: 1, 2, 7, 14

Since, 1 is the only common factor between 5 and 14. The Greatest Common Factor of 5 and 14 is 1.

GCF of 5 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 = 5

GCF(14, 5) = GCF(5, 14 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 5 and 14 is 1.

GCF of 5 and 14 by Long Division

GCF of 5 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 5 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (5) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 5 and 14.

☛ Also Check:

GCF of 5 and 14 Examples

Example 1: Find the greatest number that divides 5 and 14 exactly.

Solution:

The greatest number that divides 5 and 14 exactly is their greatest common factor, i.e. GCF of 5 and 14.
⇒ Factors of 5 and 14:
- Factors of 5 = 1, 5
- Factors of 14 = 1, 2, 7, 14
Therefore, the GCF of 5 and 14 is 1.
Example 2: For two numbers, GCF = 1 and LCM = 70. If one number is 14, find the other number.

Solution:

Given: GCF (y, 14) = 1 and LCM (y, 14) = 70
∵ GCF × LCM = 14 × (y)
⇒ y = (GCF × LCM)/14
⇒ y = (1 × 70)/14
⇒ y = 5
Therefore, the other number is 5.
Example 3: Find the GCF of 5 and 14, if their LCM is 70.

Solution:

∵ LCM × GCF = 5 × 14
⇒ GCF(5, 14) = (5 × 14)/70 = 1
Therefore, the greatest common factor of 5 and 14 is 1.

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FAQs on GCF of 5 and 14

What is the GCF of 5 and 14?

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

How to Find the GCF of 5 and 14 by Long Division Method?

To find the GCF of 5, 14 using long division method, 14 is divided by 5. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

If the GCF of 14 and 5 is 1, Find its LCM.

GCF(14, 5) × LCM(14, 5) = 14 × 5
Since the GCF of 14 and 5 = 1
⇒ 1 × LCM(14, 5) = 70
Therefore, LCM = 70
☛ Greatest Common Factor Calculator

How to Find the GCF of 5 and 14 by Prime Factorization?

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

What are the Methods to Find GCF of 5 and 14?

There are three commonly used methods to find the GCF of 5 and 14.

By Listing Common Factors
By Prime Factorization
By Long Division

What is the Relation Between LCM and GCF of 5, 14?

The following equation can be used to express the relation between LCM and GCF of 5 and 14, i.e. GCF × LCM = 5 × 14.

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