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

GCF of 44 and 48

GCF of 44 and 48 is the largest possible number that divides 44 and 48 exactly without any remainder. The factors of 44 and 48 are 1, 2, 4, 11, 22, 44 and 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 respectively. There are 3 commonly used methods to find the GCF of 44 and 48 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 44 and 48
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 44 and 48?

Answer: GCF of 44 and 48 is 4.

Explanation:

The GCF of two non-zero integers, x(44) and y(48), is the greatest positive integer m(4) that divides both x(44) and y(48) without any remainder.

Methods to Find GCF of 44 and 48

Let's look at the different methods for finding the GCF of 44 and 48.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 44 and 48 by Long Division

GCF of 44 and 48 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 48 (larger number) by 44 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (44) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 44 and 48.

GCF of 44 and 48 by Listing Common Factors

Factors of 44: 1, 2, 4, 11, 22, 44
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

There are 3 common factors of 44 and 48, that are 1, 2, and 4. Therefore, the greatest common factor of 44 and 48 is 4.

GCF of 44 and 48 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)
where X > Y and mod is the modulo operator.

Here X = 48 and Y = 44

GCF(48, 44) = GCF(44, 48 mod 44) = GCF(44, 4)
GCF(44, 4) = GCF(4, 44 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 44 and 48 is 4.

☛ Also Check:

GCF of 44 and 48 Examples

Example 1: Find the greatest number that divides 44 and 48 exactly.

Solution:

The greatest number that divides 44 and 48 exactly is their greatest common factor, i.e. GCF of 44 and 48.
⇒ Factors of 44 and 48:
- Factors of 44 = 1, 2, 4, 11, 22, 44
- Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Therefore, the GCF of 44 and 48 is 4.
Example 2: Find the GCF of 44 and 48, if their LCM is 528.

Solution:

∵ LCM × GCF = 44 × 48
⇒ GCF(44, 48) = (44 × 48)/528 = 4
Therefore, the greatest common factor of 44 and 48 is 4.
Example 3: The product of two numbers is 2112. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 2112
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2112/4
Therefore, the LCM is 528.

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 48

What is the GCF of 44 and 48?

The GCF of 44 and 48 is 4. To calculate the greatest common factor (GCF) of 44 and 48, we need to factor each number (factors of 44 = 1, 2, 4, 11, 22, 44; factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48) and choose the greatest factor that exactly divides both 44 and 48, i.e., 4.

If the GCF of 48 and 44 is 4, Find its LCM.

GCF(48, 44) × LCM(48, 44) = 48 × 44
Since the GCF of 48 and 44 = 4
⇒ 4 × LCM(48, 44) = 2112
Therefore, LCM = 528
☛ GCF Calculator

What are the Methods to Find GCF of 44 and 48?

There are three commonly used methods to find the GCF of 44 and 48.

By Long Division
By Euclidean Algorithm
By Prime Factorization

What is the Relation Between LCM and GCF of 44, 48?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 44 and 48, i.e. GCF × LCM = 44 × 48.

How to Find the GCF of 44 and 48 by Prime Factorization?

To find the GCF of 44 and 48, we will find the prime factorization of the given numbers, i.e. 44 = 2 × 2 × 11; 48 = 2 × 2 × 2 × 2 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 44 and 48. Hence, GCF(44, 48) = 2 × 2 = 4
☛ Prime Numbers

How to Find the GCF of 44 and 48 by Long Division Method?

To find the GCF of 44, 48 using long division method, 48 is divided by 44. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

Download FREE Study Materials

GCF and LCM

Math worksheets and
visual curriculum