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GCF of 14 and 30

GCF of 14 and 30 is the largest possible number that divides 14 and 30 exactly without any remainder. The factors of 14 and 30 are 1, 2, 7, 14 and 1, 2, 3, 5, 6, 10, 15, 30 respectively. There are 3 commonly used methods to find the GCF of 14 and 30 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 14 and 30
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 30?

Answer: GCF of 14 and 30 is 2.

Explanation:

The GCF of two non-zero integers, x(14) and y(30), is the greatest positive integer m(2) that divides both x(14) and y(30) without any remainder.

Methods to Find GCF of 14 and 30

Let's look at the different methods for finding the GCF of 14 and 30.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 14 and 30 by Prime Factorization

Prime factorization of 14 and 30 is (2 × 7) and (2 × 3 × 5) respectively. As visible, 14 and 30 have only one common prime factor i.e. 2. Hence, the GCF of 14 and 30 is 2.

GCF of 14 and 30 by Listing Common Factors

Factors of 14: 1, 2, 7, 14
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

There are 2 common factors of 14 and 30, that are 1 and 2. Therefore, the greatest common factor of 14 and 30 is 2.

GCF of 14 and 30 by Long Division

GCF of 14 and 30 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 30 (larger number) by 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 14 and 30.

☛ Also Check:

GCF of 14 and 30 Examples

Example 1: The product of two numbers is 420. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 420
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 420/2
Therefore, the LCM is 210.
Example 2: Find the greatest number that divides 14 and 30 exactly.

Solution:

The greatest number that divides 14 and 30 exactly is their greatest common factor, i.e. GCF of 14 and 30.
⇒ Factors of 14 and 30:
- Factors of 14 = 1, 2, 7, 14
- Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30
Therefore, the GCF of 14 and 30 is 2.
Example 3: For two numbers, GCF = 2 and LCM = 210. If one number is 30, find the other number.

Solution:

Given: GCF (z, 30) = 2 and LCM (z, 30) = 210
∵ GCF × LCM = 30 × (z)
⇒ z = (GCF × LCM)/30
⇒ z = (2 × 210)/30
⇒ z = 14
Therefore, the other number is 14.

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FAQs on GCF of 14 and 30

What is the GCF of 14 and 30?

The GCF of 14 and 30 is 2. To calculate the greatest common factor (GCF) of 14 and 30, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30) and choose the greatest factor that exactly divides both 14 and 30, i.e., 2.

What is the Relation Between LCM and GCF of 14, 30?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 14 and 30, i.e. GCF × LCM = 14 × 30.

How to Find the GCF of 14 and 30 by Long Division Method?

To find the GCF of 14, 30 using long division method, 30 is divided by 14. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 14 and 30?

There are three commonly used methods to find the GCF of 14 and 30.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 14 and 30 by Prime Factorization?

To find the GCF of 14 and 30, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 30 = 2 × 3 × 5.
⇒ Since 2 is the only common prime factor of 14 and 30. Hence, GCF (14, 30) = 2.
☛ What are Prime Numbers?

If the GCF of 30 and 14 is 2, Find its LCM.

GCF(30, 14) × LCM(30, 14) = 30 × 14
Since the GCF of 30 and 14 = 2
⇒ 2 × LCM(30, 14) = 420
Therefore, LCM = 210
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