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GCF of 8 and 32

GCF of 8 and 32 is the largest possible number that divides 8 and 32 exactly without any remainder. The factors of 8 and 32 are 1, 2, 4, 8 and 1, 2, 4, 8, 16, 32 respectively. There are 3 commonly used methods to find the GCF of 8 and 32 - long division, Euclidean algorithm, and prime factorization.

1.	GCF of 8 and 32
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 8 and 32?

Answer: GCF of 8 and 32 is 8.

Explanation:

The GCF of two non-zero integers, x(8) and y(32), is the greatest positive integer m(8) that divides both x(8) and y(32) without any remainder.

Methods to Find GCF of 8 and 32

Let's look at the different methods for finding the GCF of 8 and 32.

Prime Factorization Method
Long Division Method
Using Euclid's Algorithm

GCF of 8 and 32 by Prime Factorization

Prime factorization of 8 and 32 is (2 × 2 × 2) and (2 × 2 × 2 × 2 × 2) respectively. As visible, 8 and 32 have common prime factors. Hence, the GCF of 8 and 32 is 2 × 2 × 2 = 8.

GCF of 8 and 32 by Long Division

GCF of 8 and 32 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 32 (larger number) by 8 (smaller number).
Step 2: Since the remainder = 0, the divisor (8) is the GCF of 8 and 32.

The corresponding divisor (8) is the GCF of 8 and 32.

GCF of 8 and 32 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 = 32 and Y = 8

GCF(32, 8) = GCF(8, 32 mod 8) = GCF(8, 0)
GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 8 and 32 is 8.

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GCF of 8 and 32 Examples

Example 1: Find the GCF of 8 and 32, if their LCM is 32.

Solution:

∵ LCM × GCF = 8 × 32
⇒ GCF(8, 32) = (8 × 32)/32 = 8
Therefore, the greatest common factor of 8 and 32 is 8.
Example 2: The product of two numbers is 256. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 256
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 256/8
Therefore, the LCM is 32.
Example 3: Find the greatest number that divides 8 and 32 exactly.

Solution:

The greatest number that divides 8 and 32 exactly is their greatest common factor, i.e. GCF of 8 and 32.
⇒ Factors of 8 and 32:
- Factors of 8 = 1, 2, 4, 8
- Factors of 32 = 1, 2, 4, 8, 16, 32
Therefore, the GCF of 8 and 32 is 8.

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FAQs on GCF of 8 and 32

What is the GCF of 8 and 32?

The GCF of 8 and 32 is 8. To calculate the greatest common factor (GCF) of 8 and 32, we need to factor each number (factors of 8 = 1, 2, 4, 8; factors of 32 = 1, 2, 4, 8, 16, 32) and choose the greatest factor that exactly divides both 8 and 32, i.e., 8.

How to Find the GCF of 8 and 32 by Prime Factorization?

To find the GCF of 8 and 32, we will find the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 32 = 2 × 2 × 2 × 2 × 2.
⇒ Since 2, 2, 2 are common terms in the prime factorization of 8 and 32. Hence, GCF(8, 32) = 2 × 2 × 2 = 8
☛ Prime Number

What is the Relation Between LCM and GCF of 8, 32?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 8 and 32, i.e. GCF × LCM = 8 × 32.

How to Find the GCF of 8 and 32 by Long Division Method?

To find the GCF of 8, 32 using long division method, 32 is divided by 8. The corresponding divisor (8) when remainder equals 0 is taken as GCF.

What are the Methods to Find GCF of 8 and 32?

There are three commonly used methods to find the GCF of 8 and 32.

By Prime Factorization
By Listing Common Factors
By Long Division

If the GCF of 32 and 8 is 8, Find its LCM.

GCF(32, 8) × LCM(32, 8) = 32 × 8
Since the GCF of 32 and 8 = 8
⇒ 8 × LCM(32, 8) = 256
Therefore, LCM = 32
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