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GCF of 20 and 36

GCF of 20 and 36 is the largest possible number that divides 20 and 36 exactly without any remainder. The factors of 20 and 36 are 1, 2, 4, 5, 10, 20 and 1, 2, 3, 4, 6, 9, 12, 18, 36 respectively. There are 3 commonly used methods to find the GCF of 20 and 36 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 20 and 36
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 36?

Answer: GCF of 20 and 36 is 4.

Explanation:

The GCF of two non-zero integers, x(20) and y(36), is the greatest positive integer m(4) that divides both x(20) and y(36) without any remainder.

Methods to Find GCF of 20 and 36

Let's look at the different methods for finding the GCF of 20 and 36.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 20 and 36 by Long Division

GCF of 20 and 36 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 36 (larger number) by 20 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (20) by the remainder (16).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (4) is the GCF of 20 and 36.

GCF of 20 and 36 by Listing Common Factors

Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

There are 3 common factors of 20 and 36, that are 1, 2, and 4. Therefore, the greatest common factor of 20 and 36 is 4.

GCF of 20 and 36 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 = 36 and Y = 20

GCF(36, 20) = GCF(20, 36 mod 20) = GCF(20, 16)
GCF(20, 16) = GCF(16, 20 mod 16) = GCF(16, 4)
GCF(16, 4) = GCF(4, 16 mod 4) = GCF(4, 0)
GCF(4, 0) = 4 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 20 and 36 is 4.

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GCF of 20 and 36 Examples

Example 1: The product of two numbers is 720. If their GCF is 4, what is their LCM?

Solution:

Given: GCF = 4 and product of numbers = 720
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 720/4
Therefore, the LCM is 180.
Example 2: Find the greatest number that divides 20 and 36 exactly.

Solution:

The greatest number that divides 20 and 36 exactly is their greatest common factor, i.e. GCF of 20 and 36.
⇒ Factors of 20 and 36:
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
Therefore, the GCF of 20 and 36 is 4.
Example 3: For two numbers, GCF = 4 and LCM = 180. If one number is 20, find the other number.

Solution:

Given: GCF (y, 20) = 4 and LCM (y, 20) = 180
∵ GCF × LCM = 20 × (y)
⇒ y = (GCF × LCM)/20
⇒ y = (4 × 180)/20
⇒ y = 36
Therefore, the other number is 36.

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FAQs on GCF of 20 and 36

What is the GCF of 20 and 36?

The GCF of 20 and 36 is 4. To calculate the greatest common factor of 20 and 36, we need to factor each number (factors of 20 = 1, 2, 4, 5, 10, 20; factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36) and choose the greatest factor that exactly divides both 20 and 36, i.e., 4.

What are the Methods to Find GCF of 20 and 36?

There are three commonly used methods to find the GCF of 20 and 36.

By Prime Factorization
By Long Division
By Euclidean Algorithm

How to Find the GCF of 20 and 36 by Prime Factorization?

To find the GCF of 20 and 36, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 36 = 2 × 2 × 3 × 3.
⇒ Since 2, 2 are common terms in the prime factorization of 20 and 36. Hence, GCF(20, 36) = 2 × 2 = 4
☛ What are Prime Numbers?

How to Find the GCF of 20 and 36 by Long Division Method?

To find the GCF of 20, 36 using long division method, 36 is divided by 20. The corresponding divisor (4) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 20, 36?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 20 and 36, i.e. GCF × LCM = 20 × 36.

If the GCF of 36 and 20 is 4, Find its LCM.

GCF(36, 20) × LCM(36, 20) = 36 × 20
Since the GCF of 36 and 20 = 4
⇒ 4 × LCM(36, 20) = 720
Therefore, LCM = 180
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