GCF of 8 and 32 is the biggest possible number that divides 8 and also 32 specifically without any kind of remainder. The determinants of 8 and 32 are 1, 2, 4, 8 and also 1, 2, 4, 8, 16, 32 respectively. Tbelow are 3 generally used approaches to discover the GCF of 8 and 32 - lengthy division, Euclidean algorithm, and prime factorization.

You are watching: What is the greatest common factor of 8 and 32

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

Answer: GCF of 8 and 32 is 8.

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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 kind of remainder.


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

Prime Factorization MethodLong Division MethodUsing Euclid's Algorithm

GCF of 8 and 32 by Prime Factorization

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

GCF of 8 and 32 by Long Division

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GCF of 8 and 32 is the divisor that we get once the remainder becomes 0 after doing long department continuously.

Tip 2: Due to the fact that the remainder = 0, the divisor (8) is the GCF of 8 and also 32.

The equivalent divisor (8) is the GCF of 8 and also 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|, wright here X ≠ 0)

As such, the value of GCF of 8 and also 32 is 8.

☛ Also Check:


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 = 8Because of this, the best common element of 8 and 32 is 8.


Example 2: The product of 2 numbers is 256. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and also product of numbers = 256∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 256/8Therefore, the LCM is 32.


Example 3: Find the greatest number that divides 8 and also 32 precisely.

Solution:

The greatest number that divides 8 and 32 exactly is their biggest widespread variable, i.e. GCF of 8 and also 32.⇒ Factors of 8 and also 32:

Factors of 8 = 1, 2, 4, 8Factors 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 best common element (GCF) of 8 and 32, we need to variable each number (components of 8 = 1, 2, 4, 8; determinants of 32 = 1, 2, 4, 8, 16, 32) and pick the biggest aspect that precisely 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 also 32, we will certainly uncover the prime factorization of the provided numbers, i.e. 8 = 2 × 2 × 2; 32 = 2 × 2 × 2 × 2 × 2.⇒ Because 2, 2, 2 are widespread terms in the prime factorization of 8 and also 32. Hence, GCF(8, 32) = 2 × 2 × 2 = 8☛ Prime Number

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

The following equation deserve to be supplied to expush the relation between LCM (Least Usual Multiple) and GCF of 8 and 32, i.e. GCF × LCM = 8 × 32.

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

To find the GCF of 8, 32 making use of long division technique, 32 is split by 8. The equivalent divisor (8) when remainder amounts to 0 is taken as GCF.

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

Tbelow are three commonly offered methods to uncover the GCF of 8 and also 32.

See more: Fraction 7/60 As A Percentage, Fraction 7/60 To Decimal Number Equivalent

By Prime FactorizationBy Listing Usual FactorsBy Long Division

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

GCF(32, 8) × LCM(32, 8) = 32 × 8Due to the fact that the GCF of 32 and 8 = 8⇒ 8 × LCM(32, 8) = 256As such, LCM = 32☛ Greatest Common Factor Calculator