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

GCF of 44 and 66

GCF of 44 and 66 is the largest possible number that divides 44 and 66 exactly without any remainder. The factors of 44 and 66 are 1, 2, 4, 11, 22, 44 and 1, 2, 3, 6, 11, 22, 33, 66 respectively. There are 3 commonly used methods to find the GCF of 44 and 66 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 44 and 66
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 44 and 66?

Answer: GCF of 44 and 66 is 22.

Explanation:

The GCF of two non-zero integers, x(44) and y(66), is the greatest positive integer m(22) that divides both x(44) and y(66) without any remainder.

Methods to Find GCF of 44 and 66

The methods to find the GCF of 44 and 66 are explained below.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 44 and 66 by Prime Factorization

Prime factorization of 44 and 66 is (2 × 2 × 11) and (2 × 3 × 11) respectively. As visible, 44 and 66 have common prime factors. Hence, the GCF of 44 and 66 is 2 × 11 = 22.

GCF of 44 and 66 by Long Division

GCF of 44 and 66 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 66 (larger number) by 44 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (44) by the remainder (22).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (22) is the GCF of 44 and 66.

GCF of 44 and 66 by Listing Common Factors

Factors of 44: 1, 2, 4, 11, 22, 44
Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66

There are 4 common factors of 44 and 66, that are 1, 2, 11, and 22. Therefore, the greatest common factor of 44 and 66 is 22.

☛ Also Check:

GCF of 44 and 66 Examples

Example 1: For two numbers, GCF = 22 and LCM = 132. If one number is 66, find the other number.

Solution:

Given: GCF (z, 66) = 22 and LCM (z, 66) = 132
∵ GCF × LCM = 66 × (z)
⇒ z = (GCF × LCM)/66
⇒ z = (22 × 132)/66
⇒ z = 44
Therefore, the other number is 44.
Example 2: Find the greatest number that divides 44 and 66 exactly.

Solution:

The greatest number that divides 44 and 66 exactly is their greatest common factor, i.e. GCF of 44 and 66.
⇒ Factors of 44 and 66:
- Factors of 44 = 1, 2, 4, 11, 22, 44
- Factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66
Therefore, the GCF of 44 and 66 is 22.
Example 3: The product of two numbers is 2904. If their GCF is 22, what is their LCM?

Solution:

Given: GCF = 22 and product of numbers = 2904
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2904/22
Therefore, the LCM is 132.

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 44 and 66

What is the GCF of 44 and 66?

The GCF of 44 and 66 is 22. To calculate the GCF of 44 and 66, we need to factor each number (factors of 44 = 1, 2, 4, 11, 22, 44; factors of 66 = 1, 2, 3, 6, 11, 22, 33, 66) and choose the greatest factor that exactly divides both 44 and 66, i.e., 22.

How to Find the GCF of 44 and 66 by Long Division Method?

To find the GCF of 44, 66 using long division method, 66 is divided by 44. The corresponding divisor (22) when remainder equals 0 is taken as GCF.

How to Find the GCF of 44 and 66 by Prime Factorization?

To find the GCF of 44 and 66, we will find the prime factorization of the given numbers, i.e. 44 = 2 × 2 × 11; 66 = 2 × 3 × 11.
⇒ Since 2, 11 are common terms in the prime factorization of 44 and 66. Hence, GCF(44, 66) = 2 × 11 = 22
☛ Prime Number

If the GCF of 66 and 44 is 22, Find its LCM.

GCF(66, 44) × LCM(66, 44) = 66 × 44
Since the GCF of 66 and 44 = 22
⇒ 22 × LCM(66, 44) = 2904
Therefore, LCM = 132
☛ GCF Calculator

What is the Relation Between LCM and GCF of 44, 66?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 44 and 66, i.e. GCF × LCM = 44 × 66.

What are the Methods to Find GCF of 44 and 66?

There are three commonly used methods to find the GCF of 44 and 66.

By Long Division
By Listing Common Factors
By Prime Factorization

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum