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GCF of 14 and 36

GCF of 14 and 36 is the largest possible number that divides 14 and 36 exactly without any remainder. The factors of 14 and 36 are 1, 2, 7, 14 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 14 and 36 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 14 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 36?

Answer: GCF of 14 and 36 is 2.

Explanation:

The GCF of two non-zero integers, x(14) and y(36), is the greatest positive integer m(2) that divides both x(14) and y(36) without any remainder.

Methods to Find GCF of 14 and 36

Let's look at the different methods for finding the GCF of 14 and 36.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 14 and 36 by Prime Factorization

Prime factorization of 14 and 36 is (2 × 7) and (2 × 2 × 3 × 3) respectively. As visible, 14 and 36 have only one common prime factor i.e. 2. Hence, the GCF of 14 and 36 is 2.

GCF of 14 and 36 by Listing Common Factors

Factors of 14: 1, 2, 7, 14
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 2 common factors of 14 and 36, that are 1 and 2. Therefore, the greatest common factor of 14 and 36 is 2.

GCF of 14 and 36 by Long Division

GCF of 14 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 14 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (8).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 14 and 36.

☛ Also Check:

GCF of 14 and 36 Examples

Example 1: Find the greatest number that divides 14 and 36 exactly.

Solution:

The greatest number that divides 14 and 36 exactly is their greatest common factor, i.e. GCF of 14 and 36.
⇒ Factors of 14 and 36:
- Factors of 14 = 1, 2, 7, 14
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the GCF of 14 and 36 is 2.
Example 2: Find the GCF of 14 and 36, if their LCM is 252.

Solution:

∵ LCM × GCF = 14 × 36
⇒ GCF(14, 36) = (14 × 36)/252 = 2
Therefore, the greatest common factor of 14 and 36 is 2.
Example 3: For two numbers, GCF = 2 and LCM = 252. If one number is 14, find the other number.

Solution:

Given: GCF (x, 14) = 2 and LCM (x, 14) = 252
∵ GCF × LCM = 14 × (x)
⇒ x = (GCF × LCM)/14
⇒ x = (2 × 252)/14
⇒ x = 36
Therefore, the other number is 36.

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FAQs on GCF of 14 and 36

What is the GCF of 14 and 36?

The GCF of 14 and 36 is 2. To calculate the greatest common factor of 14 and 36, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 14 and 36, i.e., 2.

What are the Methods to Find GCF of 14 and 36?

There are three commonly used methods to find the GCF of 14 and 36.

By Long Division
By Listing Common Factors
By Prime Factorization

What is the Relation Between LCM and GCF of 14, 36?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 14 and 36, i.e. GCF × LCM = 14 × 36.

How to Find the GCF of 14 and 36 by Prime Factorization?

To find the GCF of 14 and 36, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 36 = 2 × 2 × 3 × 3.
⇒ Since 2 is the only common prime factor of 14 and 36. Hence, GCF (14, 36) = 2.
☛ Prime Numbers

If the GCF of 36 and 14 is 2, Find its LCM.

GCF(36, 14) × LCM(36, 14) = 36 × 14
Since the GCF of 36 and 14 = 2
⇒ 2 × LCM(36, 14) = 504
Therefore, LCM = 252
☛ GCF Calculator

How to Find the GCF of 14 and 36 by Long Division Method?

To find the GCF of 14, 36 using long division method, 36 is divided by 14. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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