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GCF of 5 and 10

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

1.	GCF of 5 and 10
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 5 and 10?

Answer: GCF of 5 and 10 is 5.

Explanation:

The GCF of two non-zero integers, x(5) and y(10), is the greatest positive integer m(5) that divides both x(5) and y(10) without any remainder.

Methods to Find GCF of 5 and 10

Let's look at the different methods for finding the GCF of 5 and 10.

Using Euclid's Algorithm
Long Division Method
Prime Factorization Method

GCF of 5 and 10 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 = 10 and Y = 5

GCF(10, 5) = GCF(5, 10 mod 5) = GCF(5, 0)
GCF(5, 0) = 5 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 5 and 10 is 5.

GCF of 5 and 10 by Long Division

GCF of 5 and 10 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 10 (larger number) by 5 (smaller number).
Step 2: Since the remainder = 0, the divisor (5) is the GCF of 5 and 10.

The corresponding divisor (5) is the GCF of 5 and 10.

GCF of 5 and 10 by Prime Factorization

Prime factorization of 5 and 10 is (5) and (2 × 5) respectively. As visible, 5 and 10 have only one common prime factor i.e. 5. Hence, the GCF of 5 and 10 is 5.

☛ Also Check:

GCF of 5 and 10 Examples

Example 1: Find the GCF of 5 and 10, if their LCM is 10.

Solution:

∵ LCM × GCF = 5 × 10
⇒ GCF(5, 10) = (5 × 10)/10 = 5
Therefore, the greatest common factor of 5 and 10 is 5.
Example 2: The product of two numbers is 50. If their GCF is 5, what is their LCM?

Solution:

Given: GCF = 5 and product of numbers = 50
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 50/5
Therefore, the LCM is 10.
Example 3: Find the greatest number that divides 5 and 10 exactly.

Solution:

The greatest number that divides 5 and 10 exactly is their greatest common factor, i.e. GCF of 5 and 10.
⇒ Factors of 5 and 10:
- Factors of 5 = 1, 5
- Factors of 10 = 1, 2, 5, 10
Therefore, the GCF of 5 and 10 is 5.

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FAQs on GCF of 5 and 10

What is the GCF of 5 and 10?

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

What are the Methods to Find GCF of 5 and 10?

There are three commonly used methods to find the GCF of 5 and 10.

By Long Division
By Listing Common Factors
By Prime Factorization

If the GCF of 10 and 5 is 5, Find its LCM.

GCF(10, 5) × LCM(10, 5) = 10 × 5
Since the GCF of 10 and 5 = 5
⇒ 5 × LCM(10, 5) = 50
Therefore, LCM = 10
☛ GCF Calculator

What is the Relation Between LCM and GCF of 5, 10?

The following equation can be used to express the relation between Least Common Multiple and GCF of 5 and 10, i.e. GCF × LCM = 5 × 10.

How to Find the GCF of 5 and 10 by Prime Factorization?

To find the GCF of 5 and 10, we will find the prime factorization of the given numbers, i.e. 5 = 5; 10 = 2 × 5.
⇒ Since 5 is the only common prime factor of 5 and 10. Hence, GCF (5, 10) = 5.
☛ Prime Numbers

How to Find the GCF of 5 and 10 by Long Division Method?

To find the GCF of 5, 10 using long division method, 10 is divided by 5. The corresponding divisor (5) when remainder equals 0 is taken as GCF.

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