GCF that 16 and 40 is the largest possible number the divides 16 and also 40 precisely without any remainder. The determinants of 16 and 40 space 1, 2, 4, 8, 16 and 1, 2, 4, 5, 8, 10, 20, 40 respectively. There are 3 frequently used approaches to uncover the GCF that 16 and also 40 - Euclidean algorithm, long division, and prime factorization.

You are watching: Greatest common factor of 16 and 40

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

Answer: GCF the 16 and 40 is 8.

*

Explanation:

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


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

Listing usual FactorsPrime factorization MethodUsing Euclid's Algorithm

GCF that 16 and also 40 through Listing common Factors

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

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

GCF of 16 and also 40 by element Factorization

*

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

GCF the 16 and also 40 by Euclidean Algorithm

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

Here X = 40 and also Y = 16

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

Therefore, the worth of GCF that 16 and also 40 is 8.

☛ also Check:


GCF of 16 and 40 Examples


Example 1: For 2 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 other number is 40.


Example 2: discover the greatest number that divides 16 and also 40 exactly.

Solution:

The best number that divides 16 and 40 specifically is your greatest typical factor, i.e. GCF the 16 and 40.⇒ factors of 16 and 40:

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

Therefore, the GCF the 16 and 40 is 8.


Example 3: The product of 2 numbers is 640. If their GCF is 8, what is your LCM?

Solution:

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


Show equipment >

go to slidego to slidego to slide


*


Ready to see the world through math’s eyes?
Math is in ~ the main point of everything we do. Reap solving real-world math problems in live classes and also become an experienced at everything.

Book a cost-free Trial Class


FAQs ~ above GCF the 16 and also 40

What is the GCF that 16 and 40?

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

How to find the GCF the 16 and 40 through Long department Method?

To uncover the GCF of 16, 40 utilizing long division method, 40 is separated by 16. The equivalent divisor (8) once remainder amounts to 0 is taken together GCF.

What space the approaches to discover GCF of 16 and also 40?

There space three commonly used techniques to uncover the GCF that 16 and 40.

By Listing usual FactorsBy long DivisionBy element Factorization

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

See more: How Many Calories In Malibu Coconut Rum And Nutrition Facts, Calories In Malibu Rum

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

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

To uncover the GCF that 16 and 40, we will uncover the element factorization of the given numbers, i.e. 16 = 2 × 2 × 2 × 2; 40 = 2 × 2 × 2 × 5.⇒ because 2, 2, 2 are common terms in the prime factorization that 16 and also 40. Hence, GCF(16, 40) = 2 × 2 × 2 = 8☛ What is a prime Number?

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

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