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GCF of 16 and 40

GCF of 16 and 40 is the largest possible number that divides 16 and 40 exactly without any remainder. The factors of 16 and 40 are 1, 2, 4, 8, 16 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the GCF of 16 and 40 - Euclidean algorithm, long division, and prime factorization.

1.	GCF of 16 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 40?

Answer: GCF of 16 and 40 is 8.

Explanation:

The GCF of two non-zero integers, x(16) and y(40), is the greatest positive integer m(8) that divides both x(16) and y(40) without any remainder.

Methods to Find GCF of 16 and 40

The methods to find the GCF of 16 and 40 are explained below.

Listing Common Factors
Prime Factorization Method
Using Euclid's Algorithm

GCF of 16 and 40 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 4 common factors of 16 and 40, that are 8, 1, 2, and 4. Therefore, the greatest common factor of 16 and 40 is 8.

GCF of 16 and 40 by Prime Factorization

Prime factorization of 16 and 40 is (2 × 2 × 2 × 2) and (2 × 2 × 2 × 5) respectively. As visible, 16 and 40 have common prime factors. Hence, the GCF of 16 and 40 is 2 × 2 × 2 = 8.

GCF of 16 and 40 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 = 40 and Y = 16

GCF(40, 16) = GCF(16, 40 mod 16) = GCF(16, 8)
GCF(16, 8) = GCF(8, 16 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 16 and 40 is 8.

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GCF of 16 and 40 Examples

Example 1: For two numbers, GCF = 8 and LCM = 80. If one number is 16, find the other number.

Solution:

Given: GCF (x, 16) = 8 and LCM (x, 16) = 80
∵ GCF × LCM = 16 × (x)
⇒ x = (GCF × LCM)/16
⇒ x = (8 × 80)/16
⇒ x = 40
Therefore, the other number is 40.
Example 2: Find the greatest number that divides 16 and 40 exactly.

Solution:

The greatest number that divides 16 and 40 exactly is their greatest common factor, i.e. GCF of 16 and 40.
⇒ Factors of 16 and 40:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Therefore, the GCF of 16 and 40 is 8.
Example 3: The product of two numbers is 640. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 640
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 640/8
Therefore, the LCM is 80.

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FAQs on GCF of 16 and 40

What is the GCF of 16 and 40?

The GCF of 16 and 40 is 8. To calculate the greatest common factor of 16 and 40, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 16 and 40, i.e., 8.

How to Find the GCF of 16 and 40 by Long Division Method?

To find the GCF of 16, 40 using long division method, 40 is divided by 16. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 16 and 40?

There are three commonly used methods to find the GCF of 16 and 40.

By Listing Common Factors
By Long Division
By Prime Factorization

If the GCF of 40 and 16 is 8, Find its LCM.

GCF(40, 16) × LCM(40, 16) = 40 × 16
Since the GCF of 40 and 16 = 8
⇒ 8 × LCM(40, 16) = 640
Therefore, LCM = 80
☛ Greatest Common Factor Calculator

How to Find the GCF of 16 and 40 by Prime Factorization?

To find the GCF of 16 and 40, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 16 and 40. Hence, GCF(16, 40) = 2 × 2 × 2 = 8
☛ What is a Prime Number?

What is the Relation Between LCM and GCF of 16, 40?

The following equation can be used to express the relation between LCM and GCF of 16 and 40, i.e. GCF × LCM = 16 × 40.

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