A day full of math games & activities. Find one near you.

GCF of 14 and 22

GCF of 14 and 22 is the largest possible number that divides 14 and 22 exactly without any remainder. The factors of 14 and 22 are 1, 2, 7, 14 and 1, 2, 11, 22 respectively. There are 3 commonly used methods to find the GCF of 14 and 22 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 14 and 22
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 14 and 22?

Answer: GCF of 14 and 22 is 2.

Explanation:

The GCF of two non-zero integers, x(14) and y(22), is the greatest positive integer m(2) that divides both x(14) and y(22) without any remainder.

Methods to Find GCF of 14 and 22

The methods to find the GCF of 14 and 22 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 14 and 22 by Prime Factorization

Prime factorization of 14 and 22 is (2 × 7) and (2 × 11) respectively. As visible, 14 and 22 have only one common prime factor i.e. 2. Hence, the GCF of 14 and 22 is 2.

GCF of 14 and 22 by Listing Common Factors

Factors of 14: 1, 2, 7, 14
Factors of 22: 1, 2, 11, 22

There are 2 common factors of 14 and 22, that are 1 and 2. Therefore, the greatest common factor of 14 and 22 is 2.

GCF of 14 and 22 by Long Division

GCF of 14 and 22 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 22 (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 22.

☛ Also Check:

GCF of 14 and 22 Examples

Example 1: The product of two numbers is 308. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 308
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 308/2
Therefore, the LCM is 154.
Example 2: Find the greatest number that divides 14 and 22 exactly.

Solution:

The greatest number that divides 14 and 22 exactly is their greatest common factor, i.e. GCF of 14 and 22.
⇒ Factors of 14 and 22:
- Factors of 14 = 1, 2, 7, 14
- Factors of 22 = 1, 2, 11, 22
Therefore, the GCF of 14 and 22 is 2.
Example 3: For two numbers, GCF = 2 and LCM = 154. If one number is 14, find the other number.

Solution:

Given: GCF (y, 14) = 2 and LCM (y, 14) = 154
∵ GCF × LCM = 14 × (y)
⇒ y = (GCF × LCM)/14
⇒ y = (2 × 154)/14
⇒ y = 22
Therefore, the other number is 22.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on GCF of 14 and 22

What is the GCF of 14 and 22?

The GCF of 14 and 22 is 2. To calculate the greatest common factor of 14 and 22, we need to factor each number (factors of 14 = 1, 2, 7, 14; factors of 22 = 1, 2, 11, 22) and choose the greatest factor that exactly divides both 14 and 22, i.e., 2.

If the GCF of 22 and 14 is 2, Find its LCM.

GCF(22, 14) × LCM(22, 14) = 22 × 14
Since the GCF of 22 and 14 = 2
⇒ 2 × LCM(22, 14) = 308
Therefore, LCM = 154
☛ Greatest Common Factor Calculator

How to Find the GCF of 14 and 22 by Long Division Method?

To find the GCF of 14, 22 using long division method, 22 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, 22?

The following equation can be used to express the relation between Least Common Multiple and GCF of 14 and 22, i.e. GCF × LCM = 14 × 22.

What are the Methods to Find GCF of 14 and 22?

There are three commonly used methods to find the GCF of 14 and 22.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 14 and 22 by Prime Factorization?

To find the GCF of 14 and 22, we will find the prime factorization of the given numbers, i.e. 14 = 2 × 7; 22 = 2 × 11.
⇒ Since 2 is the only common prime factor of 14 and 22. Hence, GCF (14, 22) = 2.
☛ Prime Numbers

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum