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

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

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

Answer: GCF that 8 and also 32 is 8.

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Explanation:

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


Let's look in ~ the different methods because that finding the GCF of 8 and 32.

Prime administrate MethodLong division MethodUsing Euclid's Algorithm

GCF the 8 and also 32 by prime Factorization

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

GCF the 8 and 32 by long Division

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GCF the 8 and also 32 is the divisor the we obtain when the remainder i do not care 0 after doing long department repeatedly.

Step 2: since the remainder = 0, the divisor (8) is the GCF that 8 and also 32.

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

GCF that 8 and 32 through Euclidean Algorithm

As every the Euclidean Algorithm, GCF(X, Y) = GCF(Y, X mode Y)where X > Y and mod is the modulo operator.

Here X = 32 and Y = 8

GCF(32, 8) = GCF(8, 32 mode 8) = GCF(8, 0)GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

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

☛ likewise Check:


GCF of 8 and 32 Examples


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

Solution:

∵ LCM × GCF = 8 × 32⇒ GCF(8, 32) = (8 × 32)/32 = 8Therefore, the greatest usual factor that 8 and also 32 is 8.


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

Solution:

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


Example 3: find the biggest number the divides 8 and 32 exactly.

Solution:

The best number the divides 8 and also 32 precisely is their greatest typical factor, i.e. GCF the 8 and 32.⇒ factors of 8 and 32:

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

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


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FAQs on GCF the 8 and 32

What is the GCF of 8 and 32?

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

How to find the GCF of 8 and also 32 by element Factorization?

To find the GCF that 8 and also 32, we will uncover the element factorization that 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 element factorization the 8 and also 32. Hence, GCF(8, 32) = 2 × 2 × 2 = 8☛ element Number

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

The following equation deserve to be used to express the relation in between LCM (Least typical Multiple) and also GCF the 8 and also 32, i.e. GCF × LCM = 8 × 32.

How to discover the GCF that 8 and also 32 by Long department Method?

To uncover the GCF the 8, 32 utilizing long division method, 32 is separated by 8. The corresponding divisor (8) as soon as remainder amounts to 0 is taken together GCF.

What are the approaches to discover GCF the 8 and also 32?

There room three typically used methods to discover the GCF the 8 and 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, discover its LCM.

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