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GCF of 8 and 50

GCF of 8 and 50 is the largest possible number that divides 8 and 50 exactly without any remainder. The factors of 8 and 50 are 1, 2, 4, 8 and 1, 2, 5, 10, 25, 50 respectively. There are 3 commonly used methods to find the GCF of 8 and 50 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 8 and 50
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 50?

Answer: GCF of 8 and 50 is 2.

Explanation:

The GCF of two non-zero integers, x(8) and y(50), is the greatest positive integer m(2) that divides both x(8) and y(50) without any remainder.

Methods to Find GCF of 8 and 50

Let's look at the different methods for finding the GCF of 8 and 50.

Listing Common Factors
Prime Factorization Method
Long Division Method

GCF of 8 and 50 by Listing Common Factors

Factors of 8: 1, 2, 4, 8
Factors of 50: 1, 2, 5, 10, 25, 50

There are 2 common factors of 8 and 50, that are 1 and 2. Therefore, the greatest common factor of 8 and 50 is 2.

GCF of 8 and 50 by Prime Factorization

Prime factorization of 8 and 50 is (2 × 2 × 2) and (2 × 5 × 5) respectively. As visible, 8 and 50 have only one common prime factor i.e. 2. Hence, the GCF of 8 and 50 is 2.

GCF of 8 and 50 by Long Division

GCF of 8 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 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (2).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (2) is the GCF of 8 and 50.

☛ Also Check:

GCF of 8 and 50 Examples

Example 1: Find the GCF of 8 and 50, if their LCM is 200.

Solution:

∵ LCM × GCF = 8 × 50
⇒ GCF(8, 50) = (8 × 50)/200 = 2
Therefore, the greatest common factor of 8 and 50 is 2.
Example 2: For two numbers, GCF = 2 and LCM = 200. If one number is 8, find the other number.

Solution:

Given: GCF (z, 8) = 2 and LCM (z, 8) = 200
∵ GCF × LCM = 8 × (z)
⇒ z = (GCF × LCM)/8
⇒ z = (2 × 200)/8
⇒ z = 50
Therefore, the other number is 50.
Example 3: The product of two numbers is 400. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 400
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 400/2
Therefore, the LCM is 200.

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FAQs on GCF of 8 and 50

What is the GCF of 8 and 50?

The GCF of 8 and 50 is 2. To calculate the greatest common factor (GCF) of 8 and 50, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 50 = 1, 2, 5, 10, 25, 50) and choose the greatest factor that exactly divides both 8 and 50, i.e., 2.

If the GCF of 50 and 8 is 2, Find its LCM.

GCF(50, 8) × LCM(50, 8) = 50 × 8
Since the GCF of 50 and 8 = 2
⇒ 2 × LCM(50, 8) = 400
Therefore, LCM = 200
☛ Greatest Common Factor Calculator

How to Find the GCF of 8 and 50 by Prime Factorization?

To find the GCF of 8 and 50, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 50 = 2 × 5 × 5.
⇒ Since 2 is the only common prime factor of 8 and 50. Hence, GCF (8, 50) = 2.
☛ What are Prime Numbers?

What are the Methods to Find GCF of 8 and 50?

There are three commonly used methods to find the GCF of 8 and 50.

By Prime Factorization
By Listing Common Factors
By Long Division

What is the Relation Between LCM and GCF of 8, 50?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 8 and 50, i.e. GCF × LCM = 8 × 50.

How to Find the GCF of 8 and 50 by Long Division Method?

To find the GCF of 8, 50 using long division method, 50 is divided by 8. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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