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GCF of 20 and 40

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

1.	GCF of 20 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 20 and 40?

Answer: GCF of 20 and 40 is 20.

Explanation:

The GCF of two non-zero integers, x(20) and y(40), is the greatest positive integer m(20) that divides both x(20) and y(40) without any remainder.

Methods to Find GCF of 20 and 40

Let's look at the different methods for finding the GCF of 20 and 40.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 20 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 = 20

GCF(40, 20) = GCF(20, 40 mod 20) = GCF(20, 0)
GCF(20, 0) = 20 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 20 and 40 is 20.

GCF of 20 and 40 by Prime Factorization

Prime factorization of 20 and 40 is (2 × 2 × 5) and (2 × 2 × 2 × 5) respectively. As visible, 20 and 40 have common prime factors. Hence, the GCF of 20 and 40 is 2 × 2 × 5 = 20.

GCF of 20 and 40 by Long Division

GCF of 20 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 40 (larger number) by 20 (smaller number).
Step 2: Since the remainder = 0, the divisor (20) is the GCF of 20 and 40.

The corresponding divisor (20) is the GCF of 20 and 40.

☛ Also Check:

GCF of 20 and 40 Examples

Example 1: Find the greatest number that divides 20 and 40 exactly.

Solution:

The greatest number that divides 20 and 40 exactly is their greatest common factor, i.e. GCF of 20 and 40.
⇒ Factors of 20 and 40:
- Factors of 20 = 1, 2, 4, 5, 10, 20
- Factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40
Therefore, the GCF of 20 and 40 is 20.
Example 2: Find the GCF of 20 and 40, if their LCM is 40.

Solution:

∵ LCM × GCF = 20 × 40
⇒ GCF(20, 40) = (20 × 40)/40 = 20
Therefore, the greatest common factor of 20 and 40 is 20.
Example 3: The product of two numbers is 800. If their GCF is 20, what is their LCM?

Solution:

Given: GCF = 20 and product of numbers = 800
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 800/20
Therefore, the LCM is 40.

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FAQs on GCF of 20 and 40

What is the GCF of 20 and 40?

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

How to Find the GCF of 20 and 40 by Prime Factorization?

To find the GCF of 20 and 40, we will find the prime factorization of the given numbers, i.e. 20 = 2 × 2 × 5; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 2, 5 are common terms in the prime factorization of 20 and 40. Hence, GCF(20, 40) = 2 × 2 × 5 = 20
☛ What is a Prime Number?

What are the Methods to Find GCF of 20 and 40?

There are three commonly used methods to find the GCF of 20 and 40.

By Prime Factorization
By Euclidean Algorithm
By Long Division

How to Find the GCF of 20 and 40 by Long Division Method?

To find the GCF of 20, 40 using long division method, 40 is divided by 20. The corresponding divisor (20) when remainder equals 0 is taken as GCF.

What is the Relation Between LCM and GCF of 20, 40?

The following equation can be used to express the relation between Least Common Multiple and GCF of 20 and 40, i.e. GCF × LCM = 20 × 40.

If the GCF of 40 and 20 is 20, Find its LCM.

GCF(40, 20) × LCM(40, 20) = 40 × 20
Since the GCF of 40 and 20 = 20
⇒ 20 × LCM(40, 20) = 800
Therefore, LCM = 40
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