GCF of 8 and also 32 is the biggest possible number that divides 8 and 32 precisely without any kind of remainder. The components of 8 and 32 are 1, 2, 4, 8 and also 1, 2, 4, 8, 16, 32 respectively. Tbelow are 3 generally provided methods to uncover the GCF of 8 and also 32 - long department, Euclidean algorithm, and also prime factorization.

You are watching: What is the gcf of 8 and 32

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

Answer: GCF of 8 and also 32 is 8. Explanation:

The GCF of 2 non-zero integers, x(8) and also y(32), is the greatest positive integer m(8) that divides both x(8) and y(32) without any remainder.

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

Prime Factorization MethodLong Division MethodUsing Euclid's Algorithm

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

GCF of 8 and also 32 by Long Division GCF of 8 and 32 is the divisor that we get once the remainder becomes 0 after doing long division consistently.

Step 2: Due to the fact that the remainder = 0, the divisor (8) is the GCF of 8 and also 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)wbelow X > Y and also mod is the modulo operator.

Here X = 32 and also Y = 8

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

Because of this, the value of GCF of 8 and also 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 = 8As such, the biggest common variable of 8 and also 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 = 256/8Thus, the LCM is 32.

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

Solution:

The best number that divides 8 and 32 precisely is their biggest common aspect, i.e. GCF of 8 and also 32.⇒ Factors of 8 and 32:

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

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

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FAQs on GCF of 8 and also 32

What is the GCF of 8 and 32?

The GCF of 8 and also 32 is 8. To calculate the greatest widespread variable (GCF) of 8 and also 32, we must element each number (factors of 8 = 1, 2, 4, 8; components of 32 = 1, 2, 4, 8, 16, 32) and also pick the biggest aspect that specifically divides both 8 and also 32, i.e., 8.

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

To discover the GCF of 8 and also 32, we will uncover the prime factorization of the given 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 GCF of 8, 32?

The complying with equation have the right to be provided to expush the relation in between LCM (Leastern 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 uncover the GCF of 8, 32 using long department method, 32 is divided by 8. The matching divisor (8) as soon as remainder equates to 0 is taken as GCF.

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

Tbelow are 3 frequently supplied approaches to discover 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 8 = 8⇒ 8 × LCM(32, 8) = 256As such, LCM = 32☛ Greatest Typical Factor Calculator