GCF the 14 and 21 is the largest feasible number the divides 14 and also 21 exactly without any kind of remainder. The factors of 14 and also 21 space 1, 2, 7, 14 and 1, 3, 7, 21 respectively. There room 3 commonly used techniques to uncover the GCF the 14 and also 21 - long division, Euclidean algorithm, and also prime factorization.

You are watching: Greatest common factor of 14 and 21

1.GCF the 14 and also 21
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 14 and also 21 is 7.

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Explanation:

The GCF of two non-zero integers, x(14) and y(21), is the best positive essence m(7) that divides both x(14) and y(21) without any type of remainder.


Let's look at the different methods for finding the GCF of 14 and 21.

Long department MethodListing usual FactorsPrime administrate Method

GCF of 14 and 21 by lengthy Division

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GCF of 14 and 21 is the divisor the we gain when the remainder becomes 0 after ~ doing long department repeatedly.

Step 2: since the remainder ≠ 0, we will divide the divisor of step 1 (14) by the remainder (7).Step 3: Repeat this process until the remainder = 0.

The matching divisor (7) is the GCF the 14 and also 21.

GCF that 14 and also 21 by Listing common Factors

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Factors the 14: 1, 2, 7, 14Factors of 21: 1, 3, 7, 21

There space 2 usual factors that 14 and also 21, that are 1 and 7. Therefore, the greatest common factor the 14 and 21 is 7.

GCF that 14 and also 21 by prime Factorization

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Prime administer of 14 and also 21 is (2 × 7) and (3 × 7) respectively. As visible, 14 and also 21 have only one usual prime variable i.e. 7. Hence, the GCF that 14 and 21 is 7.

☛ likewise Check:


GCF the 14 and 21 Examples


Example 1: uncover the biggest number that divides 14 and 21 exactly.

Solution:

The greatest number the divides 14 and 21 precisely is your greatest usual factor, i.e. GCF that 14 and also 21.⇒ factors of 14 and also 21:

Factors of 14 = 1, 2, 7, 14Factors of 21 = 1, 3, 7, 21

Therefore, the GCF the 14 and also 21 is 7.


Example 2: The product of 2 numbers is 294. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of number = 294∵ LCM × GCF = product that numbers⇒ LCM = Product/GCF = 294/7Therefore, the LCM is 42.


Example 3: For two numbers, GCF = 7 and also LCM = 42. If one number is 21, discover the other number.

Solution:

Given: GCF (x, 21) = 7 and also LCM (x, 21) = 42∵ GCF × LCM = 21 × (x)⇒ x = (GCF × LCM)/21⇒ x = (7 × 42)/21⇒ x = 14Therefore, the various other number is 14.


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FAQs ~ above GCF that 14 and 21

What is the GCF that 14 and also 21?

The GCF the 14 and 21 is 7. To calculation the greatest usual factor the 14 and also 21, we require to aspect each number (factors that 14 = 1, 2, 7, 14; determinants of 21 = 1, 3, 7, 21) and choose the greatest element that specifically divides both 14 and 21, i.e., 7.

If the GCF the 21 and 14 is 7, find its LCM.

GCF(21, 14) × LCM(21, 14) = 21 × 14Since the GCF of 21 and 14 = 7⇒ 7 × LCM(21, 14) = 294Therefore, LCM = 42☛ GCF Calculator

What is the Relation between LCM and GCF that 14, 21?

The following equation can be provided to to express the relation in between LCM and GCF the 14 and 21, i.e. GCF × LCM = 14 × 21.

What space the techniques to uncover GCF the 14 and 21?

There space three frequently used approaches to uncover the GCF the 14 and also 21.

See more: What Is The Empirical Formula Of The Phosphorus Bromide? ? Phosphorus Tribromide

By Euclidean AlgorithmBy lengthy DivisionBy prime Factorization

How to discover the GCF the 14 and also 21 through Long division Method?

To discover the GCF the 14, 21 using long department method, 21 is separated by 14. The matching divisor (7) as soon as remainder equals 0 is taken as GCF.

How to discover the GCF that 14 and also 21 by prime Factorization?

To uncover the GCF of 14 and 21, us will find the prime factorization the the offered numbers, i.e. 14 = 2 × 7; 21 = 3 × 7.⇒ since 7 is the only usual prime aspect of 14 and also 21. Hence, GCF (14, 21) = 7.☛ prime Number