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GCF of 16 and 80

GCF of 16 and 80 is the largest possible number that divides 16 and 80 exactly without any remainder. The factors of 16 and 80 are 1, 2, 4, 8, 16 and 1, 2, 4, 5, 8, 10, 16, 20, 40, 80 respectively. There are 3 commonly used methods to find the GCF of 16 and 80 - Euclidean algorithm, prime factorization, and long division.

1.	GCF of 16 and 80
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 80?

Answer: GCF of 16 and 80 is 16.

Explanation:

The GCF of two non-zero integers, x(16) and y(80), is the greatest positive integer m(16) that divides both x(16) and y(80) without any remainder.

Methods to Find GCF of 16 and 80

The methods to find the GCF of 16 and 80 are explained below.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 16 and 80 by Long Division

GCF of 16 and 80 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 80 (larger number) by 16 (smaller number).
Step 2: Since the remainder = 0, the divisor (16) is the GCF of 16 and 80.

The corresponding divisor (16) is the GCF of 16 and 80.

GCF of 16 and 80 by Listing Common Factors

Factors of 16: 1, 2, 4, 8, 16
Factors of 80: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

There are 5 common factors of 16 and 80, that are 1, 2, 4, 8, and 16. Therefore, the greatest common factor of 16 and 80 is 16.

GCF of 16 and 80 by Prime Factorization

Prime factorization of 16 and 80 is (2 × 2 × 2 × 2) and (2 × 2 × 2 × 2 × 5) respectively. As visible, 16 and 80 have common prime factors. Hence, the GCF of 16 and 80 is 2 × 2 × 2 × 2 = 16.

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GCF of 16 and 80 Examples

Example 1: Find the greatest number that divides 16 and 80 exactly.

Solution:

The greatest number that divides 16 and 80 exactly is their greatest common factor, i.e. GCF of 16 and 80.
⇒ Factors of 16 and 80:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
Therefore, the GCF of 16 and 80 is 16.
Example 2: For two numbers, GCF = 16 and LCM = 80. If one number is 16, find the other number.

Solution:

Given: GCF (x, 16) = 16 and LCM (x, 16) = 80
∵ GCF × LCM = 16 × (x)
⇒ x = (GCF × LCM)/16
⇒ x = (16 × 80)/16
⇒ x = 80
Therefore, the other number is 80.
Example 3: Find the GCF of 16 and 80, if their LCM is 80.

Solution:

∵ LCM × GCF = 16 × 80
⇒ GCF(16, 80) = (16 × 80)/80 = 16
Therefore, the greatest common factor of 16 and 80 is 16.

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FAQs on GCF of 16 and 80

What is the GCF of 16 and 80?

The GCF of 16 and 80 is 16. To calculate the greatest common factor of 16 and 80, we need to factor each number (factors of 16 = 1, 2, 4, 8, 16; factors of 80 = 1, 2, 4, 5, 8, 10, 16, 20, 40, 80) and choose the greatest factor that exactly divides both 16 and 80, i.e., 16.

What are the Methods to Find GCF of 16 and 80?

There are three commonly used methods to find the GCF of 16 and 80.

By Long Division
By Prime Factorization
By Euclidean Algorithm

How to Find the GCF of 16 and 80 by Prime Factorization?

To find the GCF of 16 and 80, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 80 = 2 × 2 × 2 × 2 × 5.
⇒ Since 2, 2, 2, 2 are common terms in the prime factorization of 16 and 80. Hence, GCF(16, 80) = 2 × 2 × 2 × 2 = 16
☛ Prime Number

What is the Relation Between LCM and GCF of 16, 80?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 16 and 80, i.e. GCF × LCM = 16 × 80.

How to Find the GCF of 16 and 80 by Long Division Method?

To find the GCF of 16, 80 using long division method, 80 is divided by 16. The corresponding divisor (16) when remainder equals 0 is taken as GCF.

If the GCF of 80 and 16 is 16, Find its LCM.

GCF(80, 16) × LCM(80, 16) = 80 × 16
Since the GCF of 80 and 16 = 16
⇒ 16 × LCM(80, 16) = 1280
Therefore, LCM = 80
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