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GCF of 8 and 10

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

1.	GCF of 8 and 10
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 10?

Answer: GCF of 8 and 10 is 2.

Explanation:

The GCF of two non-zero integers, x(8) and y(10), is the greatest positive integer m(2) that divides both x(8) and y(10) without any remainder.

Methods to Find GCF of 8 and 10

Let's look at the different methods for finding the GCF of 8 and 10.

Prime Factorization Method
Long Division Method
Listing Common Factors

GCF of 8 and 10 by Prime Factorization

Prime factorization of 8 and 10 is (2 × 2 × 2) and (2 × 5) respectively. As visible, 8 and 10 have only one common prime factor i.e. 2. Hence, the GCF of 8 and 10 is 2.

GCF of 8 and 10 by Long Division

GCF of 8 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 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 10.

GCF of 8 and 10 by Listing Common Factors

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

There are 2 common factors of 8 and 10, that are 1 and 2. Therefore, the greatest common factor of 8 and 10 is 2.

☛ Also Check:

GCF of 8 and 10 Examples

Example 1: For two numbers, GCF = 2 and LCM = 40. If one number is 10, find the other number.

Solution:

Given: GCF (y, 10) = 2 and LCM (y, 10) = 40
∵ GCF × LCM = 10 × (y)
⇒ y = (GCF × LCM)/10
⇒ y = (2 × 40)/10
⇒ y = 8
Therefore, the other number is 8.
Example 2: Find the greatest number that divides 8 and 10 exactly.

Solution:

The greatest number that divides 8 and 10 exactly is their greatest common factor, i.e. GCF of 8 and 10.
⇒ Factors of 8 and 10:
- Factors of 8 = 1, 2, 4, 8
- Factors of 10 = 1, 2, 5, 10
Therefore, the GCF of 8 and 10 is 2.
Example 3: The product of two numbers is 80. If their GCF is 2, what is their LCM?

Solution:

Given: GCF = 2 and product of numbers = 80
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 80/2
Therefore, the LCM is 40.

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FAQs on GCF of 8 and 10

What is the GCF of 8 and 10?

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

What is the Relation Between LCM and GCF of 8, 10?

The following equation can be used to express the relation between LCM and GCF of 8 and 10, i.e. GCF × LCM = 8 × 10.

What are the Methods to Find GCF of 8 and 10?

There are three commonly used methods to find the GCF of 8 and 10.

By Prime Factorization
By Long Division
By Listing Common Factors

How to Find the GCF of 8 and 10 by Prime Factorization?

To find the GCF of 8 and 10, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 10 = 2 × 5.
⇒ Since 2 is the only common prime factor of 8 and 10. Hence, GCF (8, 10) = 2.
☛ What are Prime Numbers?

If the GCF of 10 and 8 is 2, Find its LCM.

GCF(10, 8) × LCM(10, 8) = 10 × 8
Since the GCF of 10 and 8 = 2
⇒ 2 × LCM(10, 8) = 80
Therefore, LCM = 40
☛ GCF Calculator

How to Find the GCF of 8 and 10 by Long Division Method?

To find the GCF of 8, 10 using long division method, 10 is divided by 8. The corresponding divisor (2) when remainder equals 0 is taken as GCF.

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