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GCF of 10 and 50

GCF of 10 and 50 is the largest possible number that divides 10 and 50 exactly without any remainder. The factors of 10 and 50 are 1, 2, 5, 10 and 1, 2, 5, 10, 25, 50 respectively. There are 3 commonly used methods to find the GCF of 10 and 50 - prime factorization, Euclidean algorithm, and long division.

1.	GCF of 10 and 50
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 10 and 50?

Answer: GCF of 10 and 50 is 10.

Explanation:

The GCF of two non-zero integers, x(10) and y(50), is the greatest positive integer m(10) that divides both x(10) and y(50) without any remainder.

Methods to Find GCF of 10 and 50

The methods to find the GCF of 10 and 50 are explained below.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 10 and 50 by Listing Common Factors

Factors of 10: 1, 2, 5, 10
Factors of 50: 1, 2, 5, 10, 25, 50

There are 4 common factors of 10 and 50, that are 1, 2, 10, and 5. Therefore, the greatest common factor of 10 and 50 is 10.

GCF of 10 and 50 by Prime Factorization

Prime factorization of 10 and 50 is (2 × 5) and (2 × 5 × 5) respectively. As visible, 10 and 50 have common prime factors. Hence, the GCF of 10 and 50 is 2 × 5 = 10.

GCF of 10 and 50 by Long Division

GCF of 10 and 50 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 50 (larger number) by 10 (smaller number).
Step 2: Since the remainder = 0, the divisor (10) is the GCF of 10 and 50.

The corresponding divisor (10) is the GCF of 10 and 50.

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GCF of 10 and 50 Examples

Example 1: For two numbers, GCF = 10 and LCM = 50. If one number is 10, find the other number.

Solution:

Given: GCF (z, 10) = 10 and LCM (z, 10) = 50
∵ GCF × LCM = 10 × (z)
⇒ z = (GCF × LCM)/10
⇒ z = (10 × 50)/10
⇒ z = 50
Therefore, the other number is 50.
Example 2: Find the greatest number that divides 10 and 50 exactly.

Solution:

The greatest number that divides 10 and 50 exactly is their greatest common factor, i.e. GCF of 10 and 50.
⇒ Factors of 10 and 50:
- Factors of 10 = 1, 2, 5, 10
- Factors of 50 = 1, 2, 5, 10, 25, 50
Therefore, the GCF of 10 and 50 is 10.
Example 3: The product of two numbers is 500. If their GCF is 10, what is their LCM?

Solution:

Given: GCF = 10 and product of numbers = 500
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 500/10
Therefore, the LCM is 50.

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FAQs on GCF of 10 and 50

What is the GCF of 10 and 50?

The GCF of 10 and 50 is 10. To calculate the GCF of 10 and 50, we need to factor each number (factors of 10 = 1, 2, 5, 10; factors of 50 = 1, 2, 5, 10, 25, 50) and choose the greatest factor that exactly divides both 10 and 50, i.e., 10.

What are the Methods to Find GCF of 10 and 50?

There are three commonly used methods to find the GCF of 10 and 50.

By Long Division
By Prime Factorization
By Listing Common Factors

What is the Relation Between LCM and GCF of 10, 50?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 10 and 50, i.e. GCF × LCM = 10 × 50.

If the GCF of 50 and 10 is 10, Find its LCM.

GCF(50, 10) × LCM(50, 10) = 50 × 10
Since the GCF of 50 and 10 = 10
⇒ 10 × LCM(50, 10) = 500
Therefore, LCM = 50
☛ Greatest Common Factor Calculator

How to Find the GCF of 10 and 50 by Long Division Method?

To find the GCF of 10, 50 using long division method, 50 is divided by 10. The corresponding divisor (10) when remainder equals 0 is taken as GCF.

How to Find the GCF of 10 and 50 by Prime Factorization?

To find the GCF of 10 and 50, we will find the prime factorization of the given numbers, i.e. 10 = 2 × 5; 50 = 2 × 5 × 5.
⇒ Since 2, 5 are common terms in the prime factorization of 10 and 50. Hence, GCF(10, 50) = 2 × 5 = 10
☛ What is a Prime Number?

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