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GCF of 14 and 24

GCF of 14 and 24 is the largest possible number that divides 14 and 24 exactly without any remainder. The factors of 14 and 24 are 1, 2, 7, 14 and 1, 2, 3, 4, 6, 8, 12, 24 respectively. There are 3 commonly used methods to find the GCF of 14 and 24 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 14 and 24
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 24?

Answer: GCF of 14 and 24 is 2.

Explanation:

The GCF of two non-zero integers, x(14) and y(24), is the greatest positive integer m(2) that divides both x(14) and y(24) without any remainder.

Methods to Find GCF of 14 and 24

Let's look at the different methods for finding the GCF of 14 and 24.

Prime Factorization Method
Using Euclid's Algorithm
Listing Common Factors

GCF of 14 and 24 by Prime Factorization

Prime factorization of 14 and 24 is (2 × 7) and (2 × 2 × 2 × 3) respectively. As visible, 14 and 24 have only one common prime factor i.e. 2. Hence, the GCF of 14 and 24 is 2.

GCF of 14 and 24 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 = 24 and Y = 14

GCF(24, 14) = GCF(14, 24 mod 14) = GCF(14, 10)
GCF(14, 10) = GCF(10, 14 mod 10) = GCF(10, 4)
GCF(10, 4) = GCF(4, 10 mod 4) = GCF(4, 2)
GCF(4, 2) = GCF(2, 4 mod 2) = GCF(2, 0)
GCF(2, 0) = 2 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 14 and 24 is 2.

GCF of 14 and 24 by Listing Common Factors

Factors of 14: 1, 2, 7, 14
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

There are 2 common factors of 14 and 24, that are 1 and 2. Therefore, the greatest common factor of 14 and 24 is 2.

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GCF of 14 and 24 Examples

Example 1: For two numbers, GCF = 2 and LCM = 168. If one number is 14, find the other number.

Solution:

Given: GCF (x, 14) = 2 and LCM (x, 14) = 168
∵ GCF × LCM = 14 × (x)
⇒ x = (GCF × LCM)/14
⇒ x = (2 × 168)/14
⇒ x = 24
Therefore, the other number is 24.
Example 2: Find the greatest number that divides 14 and 24 exactly.

Solution:

The greatest number that divides 14 and 24 exactly is their greatest common factor, i.e. GCF of 14 and 24.
⇒ Factors of 14 and 24:
- Factors of 14 = 1, 2, 7, 14
- Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24
Therefore, the GCF of 14 and 24 is 2.
Example 3: Find the GCF of 14 and 24, if their LCM is 168.

Solution:

∵ LCM × GCF = 14 × 24
⇒ GCF(14, 24) = (14 × 24)/168 = 2
Therefore, the greatest common factor of 14 and 24 is 2.

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FAQs on GCF of 14 and 24

What is the GCF of 14 and 24?

The GCF of 14 and 24 is 2. To calculate the greatest common factor of 14 and 24, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24) and choose the greatest factor that exactly divides both 14 and 24, i.e., 2.

If the GCF of 24 and 14 is 2, Find its LCM.

GCF(24, 14) × LCM(24, 14) = 24 × 14
Since the GCF of 24 and 14 = 2
⇒ 2 × LCM(24, 14) = 336
Therefore, LCM = 168
☛ Greatest Common Factor Calculator

How to Find the GCF of 14 and 24 by Long Division Method?

To find the GCF of 14, 24 using long division method, 24 is divided by 14. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 14, 24?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 14 and 24, i.e. GCF × LCM = 14 × 24.

What are the Methods to Find GCF of 14 and 24?

There are three commonly used methods to find the GCF of 14 and 24.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 14 and 24 by Prime Factorization?

To find the GCF of 14 and 24, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 24 = 2 × 2 × 2 × 3.
⇒ Since 2 is the only common prime factor of 14 and 24. Hence, GCF (14, 24) = 2.
☛ What is a Prime Number?

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