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GCF of 16 and 44

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

1.	GCF of 16 and 44
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 44?

Answer: GCF of 16 and 44 is 4.

Explanation:

The GCF of two non-zero integers, x(16) and y(44), is the greatest positive integer m(4) that divides both x(16) and y(44) without any remainder.

Methods to Find GCF of 16 and 44

The methods to find the GCF of 16 and 44 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 16 and 44 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 44: 1, 2, 4, 11, 22, 44

There are 3 common factors of 16 and 44, that are 1, 2, and 4. Therefore, the greatest common factor of 16 and 44 is 4.

GCF of 16 and 44 by Prime Factorization

Prime factorization of 16 and 44 is (2 × 2 × 2 × 2) and (2 × 2 × 11) respectively. As visible, 16 and 44 have common prime factors. Hence, the GCF of 16 and 44 is 2 × 2 = 4.

GCF of 16 and 44 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 = 44 and Y = 16

GCF(44, 16) = GCF(16, 44 mod 16) = GCF(16, 12)
GCF(16, 12) = GCF(12, 16 mod 12) = GCF(12, 4)
GCF(12, 4) = GCF(4, 12 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 16 and 44 is 4.

☛ Also Check:

GCF of 16 and 44 Examples

Example 1: Find the GCF of 16 and 44, if their LCM is 176.

Solution:

∵ LCM × GCF = 16 × 44
⇒ GCF(16, 44) = (16 × 44)/176 = 4
Therefore, the greatest common factor of 16 and 44 is 4.
Example 2: The product of two numbers is 704. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 704
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 704/4
Therefore, the LCM is 176.
Example 3: Find the greatest number that divides 16 and 44 exactly.

Solution:

The greatest number that divides 16 and 44 exactly is their greatest common factor, i.e. GCF of 16 and 44.
⇒ Factors of 16 and 44:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 44 = 1, 2, 4, 11, 22, 44
Therefore, the GCF of 16 and 44 is 4.

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FAQs on GCF of 16 and 44

What is the GCF of 16 and 44?

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

How to Find the GCF of 16 and 44 by Prime Factorization?

To find the GCF of 16 and 44, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 44 = 2 × 2 × 11.
⇒ Since 2, 2 are common terms in the prime factorization of 16 and 44. Hence, GCF(16, 44) = 2 × 2 = 4
☛ Prime Numbers

What are the Methods to Find GCF of 16 and 44?

There are three commonly used methods to find the GCF of 16 and 44.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 16 and 44 by Long Division Method?

To find the GCF of 16, 44 using long division method, 44 is divided by 16. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 16, 44?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 16 and 44, i.e. GCF × LCM = 16 × 44.

If the GCF of 44 and 16 is 4, Find its LCM.

GCF(44, 16) × LCM(44, 16) = 44 × 16
Since the GCF of 44 and 16 = 4
⇒ 4 × LCM(44, 16) = 704
Therefore, LCM = 176
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