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GCF of 10 and 20

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

1.	GCF of 10 and 20
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 20?

Answer: GCF of 10 and 20 is 10.

Explanation:

The GCF of two non-zero integers, x(10) and y(20), is the greatest positive integer m(10) that divides both x(10) and y(20) without any remainder.

Methods to Find GCF of 10 and 20

Let's look at the different methods for finding the GCF of 10 and 20.

Listing Common Factors
Long Division Method
Using Euclid's Algorithm

GCF of 10 and 20 by Listing Common Factors

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

There are 4 common factors of 10 and 20, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 10 and 20 is 10.

GCF of 10 and 20 by Long Division

GCF of 10 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 10 (smaller number).
Step 2: Since the remainder = 0, the divisor (10) is the GCF of 10 and 20.

The corresponding divisor (10) is the GCF of 10 and 20.

GCF of 10 and 20 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 = 20 and Y = 10

GCF(20, 10) = GCF(10, 20 mod 10) = GCF(10, 0)
GCF(10, 0) = 10 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 10 and 20 is 10.

☛ Also Check:

GCF of 10 and 20 Examples

Example 1: Find the greatest number that divides 10 and 20 exactly.

Solution:

The greatest number that divides 10 and 20 exactly is their greatest common factor, i.e. GCF of 10 and 20.
⇒ Factors of 10 and 20:
- Factors of 10 = 1, 2, 5, 10
- Factors of 20 = 1, 2, 4, 5, 10, 20
Therefore, the GCF of 10 and 20 is 10.
Example 2: The product of two numbers is 200. If their GCF is 10, what is their LCM?

Solution:

Given: GCF = 10 and product of numbers = 200
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 200/10
Therefore, the LCM is 20.
Example 3: Find the GCF of 10 and 20, if their LCM is 20.

Solution:

∵ LCM × GCF = 10 × 20
⇒ GCF(10, 20) = (10 × 20)/20 = 10
Therefore, the greatest common factor of 10 and 20 is 10.

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FAQs on GCF of 10 and 20

What is the GCF of 10 and 20?

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

How to Find the GCF of 10 and 20 by Prime Factorization?

To find the GCF of 10 and 20, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 20 = 2 × 2 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 10 and 20. Hence, GCF(10, 20) = 2 × 5 = 10
☛ What are Prime Numbers?

If the GCF of 20 and 10 is 10, Find its LCM.

GCF(20, 10) × LCM(20, 10) = 20 × 10
Since the GCF of 20 and 10 = 10
⇒ 10 × LCM(20, 10) = 200
Therefore, LCM = 20
☛ GCF Calculator

What is the Relation Between LCM and GCF of 10, 20?

The following equation can be used to express the relation between Least Common Multiple and GCF of 10 and 20, i.e. GCF × LCM = 10 × 20.

How to Find the GCF of 10 and 20 by Long Division Method?

To find the GCF of 10, 20 using long division method, 20 is divided by 10. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 10 and 20?

There are three commonly used methods to find the GCF of 10 and 20.

By Euclidean Algorithm
By Long Division
By Prime Factorization

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