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GCF of 4 and 14

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

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

What is GCF of 4 and 14?

Answer: GCF of 4 and 14 is 2.

Explanation:

The GCF of two non-zero integers, x(4) and y(14), is the greatest positive integer m(2) that divides both x(4) and y(14) without any remainder.

Methods to Find GCF of 4 and 14

The methods to find the GCF of 4 and 14 are explained below.

Listing Common Factors
Long Division Method
Prime Factorization Method

GCF of 4 and 14 by Listing Common Factors

Factors of 4: 1, 2, 4
Factors of 14: 1, 2, 7, 14

There are 2 common factors of 4 and 14, that are 1 and 2. Therefore, the greatest common factor of 4 and 14 is 2.

GCF of 4 and 14 by Long Division

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

The corresponding divisor (2) is the GCF of 4 and 14.

GCF of 4 and 14 by Prime Factorization

Prime factorization of 4 and 14 is (2 × 2) and (2 × 7) respectively. As visible, 4 and 14 have only one common prime factor i.e. 2. Hence, the GCF of 4 and 14 is 2.

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GCF of 4 and 14 Examples

Example 1: For two numbers, GCF = 2 and LCM = 28. If one number is 14, find the other number.

Solution:

Given: GCF (x, 14) = 2 and LCM (x, 14) = 28
∵ GCF × LCM = 14 × (x)
⇒ x = (GCF × LCM)/14
⇒ x = (2 × 28)/14
⇒ x = 4
Therefore, the other number is 4.
Example 2: Find the greatest number that divides 4 and 14 exactly.

Solution:

The greatest number that divides 4 and 14 exactly is their greatest common factor, i.e. GCF of 4 and 14.
⇒ Factors of 4 and 14:
- Factors of 4 = 1, 2, 4
- Factors of 14 = 1, 2, 7, 14
Therefore, the GCF of 4 and 14 is 2.
Example 3: Find the GCF of 4 and 14, if their LCM is 28.

Solution:

∵ LCM × GCF = 4 × 14
⇒ GCF(4, 14) = (4 × 14)/28 = 2
Therefore, the greatest common factor of 4 and 14 is 2.

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FAQs on GCF of 4 and 14

What is the GCF of 4 and 14?

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

If the GCF of 14 and 4 is 2, Find its LCM.

GCF(14, 4) × LCM(14, 4) = 14 × 4
Since the GCF of 14 and 4 = 2
⇒ 2 × LCM(14, 4) = 56
Therefore, LCM = 28
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What is the Relation Between LCM and GCF of 4, 14?

The following equation can be used to express the relation between Least Common Multiple and GCF of 4 and 14, i.e. GCF × LCM = 4 × 14.

What are the Methods to Find GCF of 4 and 14?

There are three commonly used methods to find the GCF of 4 and 14.

By Long Division
By Listing Common Factors
By Prime Factorization

How to Find the GCF of 4 and 14 by Long Division Method?

To find the GCF of 4, 14 using long division method, 14 is divided by 4. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

How to Find the GCF of 4 and 14 by Prime Factorization?

To find the GCF of 4 and 14, we will find the prime factorization of the given numbers, i.e. 4 = 2 × 2; 14 = 2 × 7.
⇒ Since 2 is the only common prime factor of 4 and 14. Hence, GCF (4, 14) = 2.
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