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GCF of 8 and 125

GCF of 8 and 125 is the largest possible number that divides 8 and 125 exactly without any remainder. The factors of 8 and 125 are 1, 2, 4, 8 and 1, 5, 25, 125 respectively. There are 3 commonly used methods to find the GCF of 8 and 125 - long division, prime factorization, and Euclidean algorithm.

1.	GCF of 8 and 125
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 125?

Answer: GCF of 8 and 125 is 1.

Explanation:

The GCF of two non-zero integers, x(8) and y(125), is the greatest positive integer m(1) that divides both x(8) and y(125) without any remainder.

Methods to Find GCF of 8 and 125

Let's look at the different methods for finding the GCF of 8 and 125.

Long Division Method
Listing Common Factors
Prime Factorization Method

GCF of 8 and 125 by Long Division

GCF of 8 and 125 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 125 (larger number) by 8 (smaller number).
Step 2: Since the remainder ≠ 0, we will divide the divisor of step 1 (8) by the remainder (5).
Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (1) is the GCF of 8 and 125.

GCF of 8 and 125 by Listing Common Factors

Factors of 8: 1, 2, 4, 8
Factors of 125: 1, 5, 25, 125

Since, 1 is the only common factor between 8 and 125. The Greatest Common Factor of 8 and 125 is 1.

GCF of 8 and 125 by Prime Factorization

Prime factorization of 8 and 125 is (2 × 2 × 2) and (5 × 5 × 5) respectively. As visible, there are no common prime factors between 8 and 125, i.e. they are coprime. Hence, the GCF of 8 and 125 will be 1.

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GCF of 8 and 125 Examples

Example 1: The product of two numbers is 1000. If their GCF is 1, what is their LCM?

Solution:

Given: GCF = 1 and product of numbers = 1000
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 1000/1
Therefore, the LCM is 1000.
Example 2: Find the greatest number that divides 8 and 125 exactly.

Solution:

The greatest number that divides 8 and 125 exactly is their greatest common factor, i.e. GCF of 8 and 125.
⇒ Factors of 8 and 125:
- Factors of 8 = 1, 2, 4, 8
- Factors of 125 = 1, 5, 25, 125
Therefore, the GCF of 8 and 125 is 1.
Example 3: Find the GCF of 8 and 125, if their LCM is 1000.

Solution:

∵ LCM × GCF = 8 × 125
⇒ GCF(8, 125) = (8 × 125)/1000 = 1
Therefore, the greatest common factor of 8 and 125 is 1.

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FAQs on GCF of 8 and 125

What is the GCF of 8 and 125?

The GCF of 8 and 125 is 1. To calculate the greatest common factor (GCF) of 8 and 125, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 125 = 1, 5, 25, 125) and choose the greatest factor that exactly divides both 8 and 125, i.e., 1.

What is the Relation Between LCM and GCF of 8, 125?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 8 and 125, i.e. GCF × LCM = 8 × 125.

If the GCF of 125 and 8 is 1, Find its LCM.

GCF(125, 8) × LCM(125, 8) = 125 × 8
Since the GCF of 125 and 8 = 1
⇒ 1 × LCM(125, 8) = 1000
Therefore, LCM = 1000
☛ Greatest Common Factor Calculator

How to Find the GCF of 8 and 125 by Long Division Method?

To find the GCF of 8, 125 using long division method, 125 is divided by 8. The corresponding divisor (1) when remainder equals 0 is taken as GCF.

How to Find the GCF of 8 and 125 by Prime Factorization?

To find the GCF of 8 and 125, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 125 = 5 × 5 × 5.
⇒ There is no common prime factor for 8 and 125. Hence, GCF (8, 125) = 1.
☛ Prime Numbers

What are the Methods to Find GCF of 8 and 125?

There are three commonly used methods to find the GCF of 8 and 125.

By Long Division
By Prime Factorization
By Listing Common Factors

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