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GCF of 16 and 20

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

1.	GCF of 16 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 16 and 20?

Answer: GCF of 16 and 20 is 4.

Explanation:

The GCF of two non-zero integers, x(16) and y(20), is the greatest positive integer m(4) that divides both x(16) and y(20) without any remainder.

Methods to Find GCF of 16 and 20

The methods to find the GCF of 16 and 20 are explained below.

Prime Factorization Method
Listing Common Factors
Long Division Method

GCF of 16 and 20 by Prime Factorization

Prime factorization of 16 and 20 is (2 × 2 × 2 × 2) and (2 × 2 × 5) respectively. As visible, 16 and 20 have common prime factors. Hence, the GCF of 16 and 20 is 2 × 2 = 4.

GCF of 16 and 20 by Listing Common Factors

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

There are 3 common factors of 16 and 20, that are 1, 2, and 4. Therefore, the greatest common factor of 16 and 20 is 4.

GCF of 16 and 20 by Long Division

GCF of 16 and 20 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 20 (larger number) by 16 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (16) by the remainder (4).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 16 and 20.

☛ Also Check:

GCF of 16 and 20 Examples

Example 1: Find the greatest number that divides 16 and 20 exactly.

Solution:

The greatest number that divides 16 and 20 exactly is their greatest common factor, i.e. GCF of 16 and 20.
⇒ Factors of 16 and 20:
- Factors of 16 = 1, 2, 4, 8, 16
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 16 and 20 is 4.
Example 2: The product of two numbers is 320. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 320
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 320/4
Therefore, the LCM is 80.
Example 3: Find the GCF of 16 and 20, if their LCM is 80.

Solution:

∵ LCM × GCF = 16 × 20
⇒ GCF(16, 20) = (16 × 20)/80 = 4
Therefore, the greatest common factor of 16 and 20 is 4.

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FAQs on GCF of 16 and 20

What is the GCF of 16 and 20?

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

How to Find the GCF of 16 and 20 by Prime Factorization?

To find the GCF of 16 and 20, we will find the prime factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 20 = 2 × 2 × 5.
⇒ Since 2, 2 are common terms in the prime factorization of 16 and 20. Hence, GCF(16, 20) = 2 × 2 = 4
☛ Prime Numbers

How to Find the GCF of 16 and 20 by Long Division Method?

To find the GCF of 16, 20 using long division method, 20 is divided by 16. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

If the GCF of 20 and 16 is 4, Find its LCM.

GCF(20, 16) × LCM(20, 16) = 20 × 16
Since the GCF of 20 and 16 = 4
⇒ 4 × LCM(20, 16) = 320
Therefore, LCM = 80
☛ GCF Calculator

What is the Relation Between LCM and GCF of 16, 20?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 16 and 20, i.e. GCF × LCM = 16 × 20.

What are the Methods to Find GCF of 16 and 20?

There are three commonly used methods to find the GCF of 16 and 20.

By Long Division
By Prime Factorization
By Euclidean Algorithm

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