GCF of 8 and also 32 is the largest possible number that divides 8 and also 32 exactly without any kind of remainder. The factors of 8 and also 32 are 1, 2, 4, 8 and also 1, 2, 4, 8, 16, 32 respectively. Tbelow are 3 typically supplied methods to find the GCF of 8 and 32 - long 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 also y(32), is the biggest positive integer m(8) that divides both x(8) and y(32) without any kind of remainder.


Let's look at the various approaches for finding the GCF of 8 and also 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 also 32 is (2 × 2 × 2) and also (2 × 2 × 2 × 2 × 2) respectively. As visible, 8 and 32 have actually common prime components. 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 also 32 is the divisor that we obtain once the remainder becomes 0 after doing long department continuously.

Step 2: Since the remainder = 0, the divisor (8) is the GCF of 8 and 32.

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

GCF of 8 and also 32 by Euclidean Algorithm

As per the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mod Y)wbelow 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|, wbelow X ≠ 0)

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

☛ Also Check:


GCF of 8 and also 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 greatest widespread aspect of 8 and also 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 = 256/8Thus, the LCM is 32.


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

Solution:

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

Factors of 8 = 1, 2, 4, 8Factors of 32 = 1, 2, 4, 8, 16, 32

As such, 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 also 32?

The GCF of 8 and 32 is 8. To calculate the biggest common factor (GCF) of 8 and also 32, we need to factor each number (components of 8 = 1, 2, 4, 8; determinants of 32 = 1, 2, 4, 8, 16, 32) and select the best factor that precisely divides both 8 and also 32, i.e., 8.

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

To uncover the GCF of 8 and 32, we will uncover the prime factorization of the given numbers, i.e. 8 = 2 × 2 × 2; 32 = 2 × 2 × 2 × 2 × 2.⇒ Due to the fact that 2, 2, 2 are common 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 adhering to equation deserve to be used to express the relation between LCM (Least Common Multiple) and GCF of 8 and also 32, i.e. GCF × LCM = 8 × 32.

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

To uncover the GCF of 8, 32 utilizing lengthy department technique, 32 is divided by 8. The matching divisor (8) once remainder equals 0 is taken as GCF.

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

Tbelow are 3 frequently used techniques to uncover the GCF of 8 and 32.

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By Prime FactorizationBy Listing Typical FactorsBy Long Division

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

GCF(32, 8) × LCM(32, 8) = 32 × 8Since the GCF of 32 and also 8 = 8⇒ 8 × LCM(32, 8) = 256Therefore, LCM = 32☛ Greatest Typical Factor Calculator