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

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1.GCF of 8 and 16
2.List that Methods
3.Solved Examples
4.FAQs

Answer: GCF the 8 and 16 is 8.

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Explanation:

The GCF of two non-zero integers, x(8) and y(16), is the biggest positive essence m(8) the divides both x(8) and also y(16) without any remainder.


Let's look at the different methods for finding the GCF the 8 and also 16.

Prime administrate MethodUsing Euclid's AlgorithmLong division Method

GCF that 8 and also 16 by prime Factorization

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Prime factorization of 8 and also 16 is (2 × 2 × 2) and (2 × 2 × 2 × 2) respectively. As visible, 8 and also 16 have usual prime factors. Hence, the GCF that 8 and also 16 is 2 × 2 × 2 = 8.

GCF the 8 and also 16 by Euclidean Algorithm

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

Here X = 16 and Y = 8

GCF(16, 8) = GCF(8, 16 mod 8) = GCF(8, 0)GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, whereby X ≠ 0)

Therefore, the value of GCF of 8 and 16 is 8.

GCF that 8 and 16 by lengthy Division

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GCF of 8 and 16 is the divisor that we obtain when the remainder becomes 0 ~ doing long department repeatedly.

Step 2: because the remainder = 0, the divisor (8) is the GCF the 8 and also 16.

The corresponding divisor (8) is the GCF of 8 and also 16.

☛ also Check:


GCF of 8 and 16 Examples


Example 1: For two numbers, GCF = 8 and LCM = 16. If one number is 8, discover the various other number.

Solution:

Given: GCF (y, 8) = 8 and also LCM (y, 8) = 16∵ GCF × LCM = 8 × (y)⇒ y = (GCF × LCM)/8⇒ y = (8 × 16)/8⇒ y = 16Therefore, the other number is 16.


Example 2: The product of 2 numbers is 128. If their GCF is 8, what is their LCM?

Solution:

Given: GCF = 8 and product of numbers = 128∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 128/8Therefore, the LCM is 16.


Example 3: uncover the biggest number that divides 8 and also 16 exactly.

Solution:

The greatest number the divides 8 and also 16 precisely is your greatest typical factor, i.e. GCF the 8 and 16.⇒ components of 8 and 16:

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

Therefore, the GCF the 8 and 16 is 8.


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FAQs on GCF of 8 and 16

What is the GCF of 8 and also 16?

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

What is the Relation in between LCM and also GCF of 8, 16?

The adhering to equation have the right to be supplied to express the relation between LCM (Least usual Multiple) and also GCF that 8 and 16, i.e. GCF × LCM = 8 × 16.

How to find the GCF that 8 and also 16 by prime Factorization?

To uncover the GCF the 8 and 16, we will uncover the prime factorization of the offered numbers, i.e. 8 = 2 × 2 × 2; 16 = 2 × 2 × 2 × 2.⇒ since 2, 2, 2 are common terms in the prime factorization of 8 and 16. Hence, GCF(8, 16) = 2 × 2 × 2 = 8☛ What is a prime Number?

How to find the GCF that 8 and also 16 by Long division Method?

To discover the GCF of 8, 16 making use of long division method, 16 is separated by 8. The corresponding divisor (8) once remainder equates to 0 is taken together GCF.

What are the techniques to uncover GCF of 8 and 16?

There are three generally used approaches to discover the GCF that 8 and also 16.

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By element FactorizationBy Euclidean AlgorithmBy long Division

If the GCF that 16 and 8 is 8, uncover its LCM.

GCF(16, 8) × LCM(16, 8) = 16 × 8Since the GCF that 16 and 8 = 8⇒ 8 × LCM(16, 8) = 128Therefore, LCM = 16☛ Greatest typical Factor Calculator