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GCF of 8 and 40

GCF of 8 and 40 is the largest possible number that divides 8 and 40 exactly without any remainder. The factors of 8 and 40 are 1, 2, 4, 8 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 commonly used methods to find the GCF of 8 and 40 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 8 and 40
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 40?

Answer: GCF of 8 and 40 is 8.

Explanation:

The GCF of two non-zero integers, x(8) and y(40), is the greatest positive integer m(8) that divides both x(8) and y(40) without any remainder.

Methods to Find GCF of 8 and 40

The methods to find the GCF of 8 and 40 are explained below.

Using Euclid's Algorithm
Prime Factorization Method
Long Division Method

GCF of 8 and 40 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 = 40 and Y = 8

GCF(40, 8) = GCF(8, 40 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 8 and 40 is 8.

GCF of 8 and 40 by Prime Factorization

Prime factorization of 8 and 40 is (2 × 2 × 2) and (2 × 2 × 2 × 5) respectively. As visible, 8 and 40 have common prime factors. Hence, the GCF of 8 and 40 is 2 × 2 × 2 = 8.

GCF of 8 and 40 by Long Division

GCF of 8 and 40 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 40 (larger number) by 8 (smaller number).
Step 2: Since the remainder = 0, the divisor (8) is the GCF of 8 and 40.

The corresponding divisor (8) is the GCF of 8 and 40.

☛ Also Check:

GCF of 8 and 40 Examples

Example 1: The product of two numbers is 320. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 320
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 320/8
Therefore, the LCM is 40.
Example 2: For two numbers, GCF = 8 and LCM = 40. If one number is 40, find the other number.

Solution:

Given: GCF (x, 40) = 8 and LCM (x, 40) = 40
∵ GCF × LCM = 40 × (x)
⇒ x = (GCF × LCM)/40
⇒ x = (8 × 40)/40
⇒ x = 8
Therefore, the other number is 8.
Example 3: Find the GCF of 8 and 40, if their LCM is 40.

Solution:

∵ LCM × GCF = 8 × 40
⇒ GCF(8, 40) = (8 × 40)/40 = 8
Therefore, the greatest common factor of 8 and 40 is 8.

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FAQs on GCF of 8 and 40

What is the GCF of 8 and 40?

The GCF of 8 and 40 is 8. To calculate the GCF of 8 and 40, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and choose the greatest factor that exactly divides both 8 and 40, i.e., 8.

If the GCF of 40 and 8 is 8, Find its LCM.

GCF(40, 8) × LCM(40, 8) = 40 × 8
Since the GCF of 40 and 8 = 8
⇒ 8 × LCM(40, 8) = 320
Therefore, LCM = 40
☛ Greatest Common Factor Calculator

How to Find the GCF of 8 and 40 by Long Division Method?

To find the GCF of 8, 40 using long division method, 40 is divided by 8. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

How to Find the GCF of 8 and 40 by Prime Factorization?

To find the GCF of 8 and 40, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 40 = 2 × 2 × 2 × 5.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 8 and 40. Hence, GCF(8, 40) = 2 × 2 × 2 = 8
☛ What are Prime Numbers?

What is the Relation Between LCM and GCF of 8, 40?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 8 and 40, i.e. GCF × LCM = 8 × 40.

What are the Methods to Find GCF of 8 and 40?

There are three commonly used methods to find the GCF of 8 and 40.

By Prime Factorization
By Long Division
By Euclidean Algorithm

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