GCF the 16 and also 40 is the largest possible number that divides 16 and 40 exactly without any remainder. The components of 16 and 40 room 1, 2, 4, 8, 16 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There space 3 typically used methods to find the GCF the 16 and 40 - Euclidean algorithm, long division, and also prime factorization.

You are watching: What is the gcf of 16 and 40

1.GCF of 16 and also 40
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 16 and also 40 is 8.

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Explanation:

The GCF of 2 non-zero integers, x(16) and y(40), is the biggest positive essence m(8) that divides both x(16) and y(40) without any remainder.


The techniques to find the GCF the 16 and 40 are explained below.

Listing usual FactorsPrime administrate MethodUsing Euclid's Algorithm

GCF the 16 and 40 by Listing typical Factors

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Factors that 16: 1, 2, 4, 8, 16Factors the 40: 1, 2, 4, 5, 8, 10, 20, 40

There are 4 typical factors the 16 and 40, that space 8, 1, 2, and 4. Therefore, the greatest usual factor that 16 and also 40 is 8.

GCF of 16 and 40 by prime Factorization

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Prime administer of 16 and also 40 is (2 × 2 × 2 × 2) and (2 × 2 × 2 × 5) respectively. Together visible, 16 and also 40 have typical prime factors. Hence, the GCF of 16 and 40 is 2 × 2 × 2 = 8.

GCF of 16 and also 40 by Euclidean Algorithm

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

Here X = 40 and Y = 16

GCF(40, 16) = GCF(16, 40 mod 16) = GCF(16, 8)GCF(16, 8) = GCF(8, 16 mode 8) = GCF(8, 0)GCF(8, 0) = 8 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the value of GCF of 16 and 40 is 8.

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GCF that 16 and 40 Examples


Example 1: For two numbers, GCF = 8 and also LCM = 80. If one number is 16, find the other number.

Solution:

Given: GCF (x, 16) = 8 and LCM (x, 16) = 80∵ GCF × LCM = 16 × (x)⇒ x = (GCF × LCM)/16⇒ x = (8 × 80)/16⇒ x = 40Therefore, the various other number is 40.


Example 2: uncover the best number the divides 16 and also 40 exactly.

Solution:

The biggest number the divides 16 and also 40 specifically is their greatest usual factor, i.e. GCF of 16 and 40.⇒ components of 16 and also 40:

Factors that 16 = 1, 2, 4, 8, 16Factors that 40 = 1, 2, 4, 5, 8, 10, 20, 40

Therefore, the GCF of 16 and 40 is 8.


Example 3: The product of two numbers is 640. If their GCF is 8, what is your LCM?

Solution:

Given: GCF = 8 and also product of number = 640∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 640/8Therefore, the LCM is 80.


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FAQs on GCF that 16 and 40

What is the GCF the 16 and also 40?

The GCF of 16 and 40 is 8. To calculation the greatest usual factor that 16 and 40, we need to factor each number (factors that 16 = 1, 2, 4, 8, 16; determinants of 40 = 1, 2, 4, 5, 8, 10, 20, 40) and also choose the greatest variable that specifically divides both 16 and 40, i.e., 8.

How to discover the GCF of 16 and 40 through Long division Method?

To discover the GCF the 16, 40 utilizing long division method, 40 is separated by 16. The matching divisor (8) as soon as remainder equates to 0 is taken as GCF.

What are the methods to discover GCF of 16 and 40?

There space three commonly used methods to discover the GCF of 16 and 40.

By Listing typical FactorsBy lengthy DivisionBy prime Factorization

If the GCF that 40 and also 16 is 8, uncover its LCM.

See more: What Is The Measure Of Each Exterior Angle Of A Regular Dodecagon ?

GCF(40, 16) × LCM(40, 16) = 40 × 16Since the GCF of 40 and 16 = 8⇒ 8 × LCM(40, 16) = 640Therefore, LCM = 80☛ Greatest typical Factor Calculator

How to uncover the GCF of 16 and also 40 by prime Factorization?

To discover the GCF that 16 and also 40, us will discover the prime factorization of the offered numbers, i.e. 16 = 2 × 2 × 2 × 2; 40 = 2 × 2 × 2 × 5.⇒ since 2, 2, 2 are usual terms in the element factorization of 16 and also 40. Hence, GCF(16, 40) = 2 × 2 × 2 = 8☛ What is a prime Number?

What is the Relation between LCM and also GCF of 16, 40?

The complying with equation deserve to be offered to express the relation in between LCM and GCF that 16 and 40, i.e. GCF × LCM = 16 × 40.