GCF that 8 and 32 is the largest possible number that divides 8 and also 32 precisely without any kind of remainder. The factors of 8 and 32 are 1, 2, 4, 8 and 1, 2, 4, 8, 16, 32 respectively. There space 3 typically used techniques to discover the GCF the 8 and also 32 - lengthy division, Euclidean algorithm, and also prime factorization.

You are watching: Greatest common factor of 8 and 32

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

Answer: GCF of 8 and 32 is 8.

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Explanation:

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


Let's look in ~ the various methods for finding the GCF the 8 and also 32.

Prime factorization MethodLong department MethodUsing Euclid's Algorithm

GCF the 8 and 32 by prime Factorization

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

GCF the 8 and also 32 by lengthy Division

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

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

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

GCF the 8 and 32 by Euclidean Algorithm

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

Here X = 32 and also Y = 8

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

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

☛ additionally Check:


GCF of 8 and 32 Examples


Example 1: discover the GCF the 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 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: discover the biggest number the divides 8 and also 32 exactly.

Solution:

The best number the divides 8 and 32 exactly is their greatest common factor, i.e. GCF of 8 and 32.⇒ components of 8 and 32:

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

Therefore, the GCF of 8 and 32 is 8.


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FAQs on GCF that 8 and also 32

What is the GCF that 8 and 32?

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

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

To discover the GCF of 8 and 32, us will discover the element factorization of the provided 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 the 8 and 32. Hence, GCF(8, 32) = 2 × 2 × 2 = 8☛ prime Number

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

The complying with equation have the right to be offered to refer the relation in between LCM (Least common Multiple) and also GCF the 8 and also 32, i.e. GCF × LCM = 8 × 32.

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

To find the GCF the 8, 32 making use of long department method, 32 is divided by 8. The corresponding divisor (8) when remainder amounts to 0 is taken together GCF.

What are the methods to find GCF that 8 and 32?

There are three typically used methods to uncover the GCF the 8 and 32.

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By element FactorizationBy Listing common FactorsBy long Division

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

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