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

GCF of 11 and 44

GCF of 11 and 44 is the largest possible number that divides 11 and 44 exactly without any remainder. The factors of 11 and 44 are 1, 11 and 1, 2, 4, 11, 22, 44 respectively. There are 3 commonly used methods to find the GCF of 11 and 44 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 11 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 11 and 44?

Answer: GCF of 11 and 44 is 11.

Explanation:

The GCF of two non-zero integers, x(11) and y(44), is the greatest positive integer m(11) that divides both x(11) and y(44) without any remainder.

Methods to Find GCF of 11 and 44

The methods to find the GCF of 11 and 44 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 11 and 44 by Long Division

GCF of 11 and 44 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 44 (larger number) by 11 (smaller number).
Step 2: Since the remainder = 0, the divisor (11) is the GCF of 11 and 44.

The corresponding divisor (11) is the GCF of 11 and 44.

GCF of 11 and 44 by Listing Common Factors

Factors of 11: 1, 11
Factors of 44: 1, 2, 4, 11, 22, 44

There are 2 common factors of 11 and 44, that are 1 and 11. Therefore, the greatest common factor of 11 and 44 is 11.

GCF of 11 and 44 by Prime Factorization

Prime factorization of 11 and 44 is (11) and (2 × 2 × 11) respectively. As visible, 11 and 44 have only one common prime factor i.e. 11. Hence, the GCF of 11 and 44 is 11.

☛ Also Check:

GCF of 11 and 44 Examples

Example 1: Find the GCF of 11 and 44, if their LCM is 44.

Solution:

∵ LCM × GCF = 11 × 44
⇒ GCF(11, 44) = (11 × 44)/44 = 11
Therefore, the greatest common factor of 11 and 44 is 11.
Example 2: The product of two numbers is 484. If their GCF is 11, what is their LCM?

Solution:

Given: GCF = 11 and product of numbers = 484
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 484/11
Therefore, the LCM is 44.
Example 3: Find the greatest number that divides 11 and 44 exactly.

Solution:

The greatest number that divides 11 and 44 exactly is their greatest common factor, i.e. GCF of 11 and 44.
⇒ Factors of 11 and 44:
- Factors of 11 = 1, 11
- Factors of 44 = 1, 2, 4, 11, 22, 44
Therefore, the GCF of 11 and 44 is 11.

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 11 and 44

What is the GCF of 11 and 44?

The GCF of 11 and 44 is 11. To calculate the greatest common factor (GCF) of 11 and 44, we need to factor each number (factors of 11 = 1, 11; factors of 44 = 1, 2, 4, 11, 22, 44) and choose the greatest factor that exactly divides both 11 and 44, i.e., 11.

How to Find the GCF of 11 and 44 by Prime Factorization?

To find the GCF of 11 and 44, we will find the prime factorization of the given numbers, i.e. 11 = 11; 44 = 2 × 2 × 11.
⇒ Since 11 is the only common prime factor of 11 and 44. Hence, GCF (11, 44) = 11.
☛ What is a Prime Number?

If the GCF of 44 and 11 is 11, Find its LCM.

GCF(44, 11) × LCM(44, 11) = 44 × 11
Since the GCF of 44 and 11 = 11
⇒ 11 × LCM(44, 11) = 484
Therefore, LCM = 44
☛ GCF Calculator

What are the Methods to Find GCF of 11 and 44?

There are three commonly used methods to find the GCF of 11 and 44.

By Prime Factorization
By Long Division
By Euclidean Algorithm

What is the Relation Between LCM and GCF of 11, 44?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 11 and 44, i.e. GCF × LCM = 11 × 44.

How to Find the GCF of 11 and 44 by Long Division Method?

To find the GCF of 11, 44 using long division method, 44 is divided by 11. The corresponding divisor (11) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum