GCF of 14 and also 28 is the largest feasible number the divides 14 and 28 exactly without any type of remainder. The components of 14 and also 28 room 1, 2, 7, 14 and also 1, 2, 4, 7, 14, 28 respectively. There are 3 frequently used approaches to find the GCF of 14 and also 28 - lengthy division, Euclidean algorithm, and prime factorization.

You are watching: What is the gcf of 14 and 28

1.GCF of 14 and also 28
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF of 14 and 28 is 14.

*

Explanation:

The GCF of 2 non-zero integers, x(14) and y(28), is the best positive creature m(14) that divides both x(14) and also y(28) without any kind of remainder.


The methods to find the GCF the 14 and 28 are described below.

Using Euclid's AlgorithmLong department MethodPrime administer Method

GCF of 14 and 28 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 = 28 and also Y = 14

GCF(28, 14) = GCF(14, 28 mod 14) = GCF(14, 0)GCF(14, 0) = 14 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the worth of GCF that 14 and also 28 is 14.

GCF the 14 and also 28 by lengthy Division

*

GCF of 14 and 28 is the divisor that we acquire when the remainder becomes 0 after doing long department repeatedly.

Step 2: because the remainder = 0, the divisor (14) is the GCF that 14 and also 28.

The corresponding divisor (14) is the GCF the 14 and also 28.

GCF the 14 and 28 by prime Factorization

*

Prime administrate of 14 and 28 is (2 × 7) and also (2 × 2 × 7) respectively. As visible, 14 and also 28 have usual prime factors. Hence, the GCF that 14 and 28 is 2 × 7 = 14.

☛ additionally Check:


GCF of 14 and 28 Examples


Example 1: For two numbers, GCF = 14 and also LCM = 28. If one number is 28, find the various other number.

Solution:

Given: GCF (y, 28) = 14 and LCM (y, 28) = 28∵ GCF × LCM = 28 × (y)⇒ y = (GCF × LCM)/28⇒ y = (14 × 28)/28⇒ y = 14Therefore, the other number is 14.


Example 2: uncover the GCF the 14 and 28, if their LCM is 28.

Solution:

∵ LCM × GCF = 14 × 28⇒ GCF(14, 28) = (14 × 28)/28 = 14Therefore, the greatest common factor of 14 and also 28 is 14.


Example 3: discover the biggest number the divides 14 and also 28 exactly.

Solution:

The best number that divides 14 and also 28 exactly is your greatest typical factor, i.e. GCF the 14 and 28.⇒ determinants of 14 and also 28:

Factors the 14 = 1, 2, 7, 14Factors that 28 = 1, 2, 4, 7, 14, 28

Therefore, the GCF that 14 and 28 is 14.


Show systems >

go come slidego to slidego come slide


*


Ready to view the world through math’s eyes?
Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an experienced at everything.

Book a cost-free Trial Class


FAQs top top GCF the 14 and also 28

What is the GCF the 14 and also 28?

The GCF the 14 and 28 is 14. To calculation the GCF of 14 and also 28, we need to aspect each number (factors the 14 = 1, 2, 7, 14; factors of 28 = 1, 2, 4, 7, 14, 28) and choose the greatest element that specifically divides both 14 and also 28, i.e., 14.

What room the techniques to find GCF the 14 and also 28?

There space three frequently used techniques to find the GCF of 14 and also 28.

By prime FactorizationBy long DivisionBy Listing usual Factors

If the GCF that 28 and 14 is 14, find its LCM.

GCF(28, 14) × LCM(28, 14) = 28 × 14Since the GCF of 28 and also 14 = 14⇒ 14 × LCM(28, 14) = 392Therefore, LCM = 28☛ GCF Calculator

How to uncover the GCF of 14 and also 28 by element Factorization?

To uncover the GCF the 14 and also 28, we will uncover the prime factorization the the given numbers, i.e. 14 = 2 × 7; 28 = 2 × 2 × 7.⇒ since 2, 7 are typical terms in the element factorization of 14 and 28. Hence, GCF(14, 28) = 2 × 7 = 14☛ What are Prime Numbers?

What is the Relation between LCM and GCF that 14, 28?

The complying with equation can be supplied to to express the relation in between Least common Multiple and also GCF of 14 and 28, i.e. GCF × LCM = 14 × 28.

See more: Where To Withdraw Money From Emerald Card ® Atm Locations, Where Can I Withdraw Money From My Emerald Card

How to find the GCF of 14 and 28 by Long department Method?

To uncover the GCF the 14, 28 utilizing long division method, 28 is separated by 14. The corresponding divisor (14) when remainder equates to 0 is taken as GCF.