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GCF of 14 and 28

GCF of 14 and 28 is the largest possible number that divides 14 and 28 exactly without any remainder. The factors of 14 and 28 are 1, 2, 7, 14 and 1, 2, 4, 7, 14, 28 respectively. There are 3 commonly used methods to find the GCF of 14 and 28 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 14 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 28?

Answer: GCF of 14 and 28 is 14.

Explanation:

The GCF of two non-zero integers, x(14) and y(28), is the greatest positive integer m(14) that divides both x(14) and y(28) without any remainder.

Methods to Find GCF of 14 and 28

The methods to find the GCF of 14 and 28 are explained below.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 14 and 28 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 = 28 and Y = 14

GCF(28, 14) = GCF(14, 28 mod 14) = GCF(14, 0)
GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 14 and 28 is 14.

GCF of 14 and 28 by Long Division

GCF of 14 and 28 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 28 (larger number) by 14 (smaller number).
Step 2: Since the remainder = 0, the divisor (14) is the GCF of 14 and 28.

The corresponding divisor (14) is the GCF of 14 and 28.

GCF of 14 and 28 by Prime Factorization

Prime factorization of 14 and 28 is (2 × 7) and (2 × 2 × 7) respectively. As visible, 14 and 28 have common prime factors. Hence, the GCF of 14 and 28 is 2 × 7 = 14.

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GCF of 14 and 28 Examples

Example 1: For two numbers, GCF = 14 and LCM = 28. If one number is 28, find the other number.

Solution:

Given: GCF (y, 28) = 14 and LCM (y, 28) = 28
∵ GCF × LCM = 28 × (y)
⇒ y = (GCF × LCM)/28
⇒ y = (14 × 28)/28
⇒ y = 14
Therefore, the other number is 14.
Example 2: Find the GCF of 14 and 28, if their LCM is 28.

Solution:

∵ LCM × GCF = 14 × 28
⇒ GCF(14, 28) = (14 × 28)/28 = 14
Therefore, the greatest common factor of 14 and 28 is 14.
Example 3: Find the greatest number that divides 14 and 28 exactly.

Solution:

The greatest number that divides 14 and 28 exactly is their greatest common factor, i.e. GCF of 14 and 28.
⇒ Factors of 14 and 28:
- Factors of 14 = 1, 2, 7, 14
- Factors of 28 = 1, 2, 4, 7, 14, 28
Therefore, the GCF of 14 and 28 is 14.

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FAQs on GCF of 14 and 28

What is the GCF of 14 and 28?

The GCF of 14 and 28 is 14. To calculate the GCF of 14 and 28, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest factor that exactly divides both 14 and 28, i.e., 14.

What are the Methods to Find GCF of 14 and 28?

There are three commonly used methods to find the GCF of 14 and 28.

By Prime Factorization
By Long Division
By Listing Common Factors

If the GCF of 28 and 14 is 14, Find its LCM.

GCF(28, 14) × LCM(28, 14) = 28 × 14
Since the GCF of 28 and 14 = 14
⇒ 14 × LCM(28, 14) = 392
Therefore, LCM = 28
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How to Find the GCF of 14 and 28 by Prime Factorization?

To find the GCF of 14 and 28, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 28 = 2 × 2 × 7.
⇒ Since 2, 7 are common terms in the prime factorization of 14 and 28. Hence, GCF(14, 28) = 2 × 7 = 14
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 14, 28?

The following equation can be used to express the relation between Least Common Multiple and GCF of 14 and 28, i.e. GCF × LCM = 14 × 28.

How to Find the GCF of 14 and 28 by Long Division Method?

To find the GCF of 14, 28 using long division method, 28 is divided by 14. The corresponding divisor (14) when remainder equals 0 is taken as GCF.

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