GCF the 14 and 21 is the largest possible number that divides 14 and also 21 specifically without any type of remainder. The determinants of 14 and also 21 are 1, 2, 7, 14 and 1, 3, 7, 21 respectively. There space 3 typically used methods to uncover the GCF of 14 and 21 - lengthy division, Euclidean algorithm, and prime factorization.

You are watching: What is the greatest common factor of 14 and 21

1.GCF of 14 and also 21
2.List that 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 also y(21), is the biggest positive creature m(7) the divides both x(14) and also y(21) without any remainder.


Let's look at the various methods for finding the GCF that 14 and also 21.

Long division MethodListing common FactorsPrime administrate Method

GCF the 14 and also 21 by lengthy Division

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GCF of 14 and also 21 is the divisor the we get when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: due to the fact that the remainder ≠ 0, we will certainly divide the divisor of action 1 (14) by the remainder (7).Step 3: Repeat this process until the remainder = 0.

The corresponding divisor (7) is the GCF of 14 and 21.

GCF of 14 and 21 through Listing usual Factors

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Factors that 14: 1, 2, 7, 14Factors that 21: 1, 3, 7, 21

There space 2 typical factors the 14 and 21, that room 1 and also 7. Therefore, the greatest typical factor of 14 and also 21 is 7.

GCF the 14 and 21 by element 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 common prime variable i.e. 7. Hence, the GCF of 14 and 21 is 7.

☛ likewise Check:


GCF that 14 and 21 Examples


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

Solution:

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

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

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


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

Solution:

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


Example 3: For 2 numbers, GCF = 7 and also LCM = 42. If one number is 21, find the various other number.

Solution:

Given: GCF (x, 21) = 7 and 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 on GCF the 14 and also 21

What is the GCF of 14 and 21?

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

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

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

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

The complying with equation have the right to be supplied to to express the relation between LCM and GCF of 14 and 21, i.e. GCF × LCM = 14 × 21.

What space the approaches to find GCF the 14 and also 21?

There room three commonly used techniques to uncover the GCF that 14 and also 21.

See more: Do You Know How To Say Very In French Translation Of “Very”, French Translation Of “Very”

By Euclidean AlgorithmBy lengthy DivisionBy prime Factorization

How to find the GCF that 14 and 21 by Long department Method?

To discover the GCF that 14, 21 utilizing long department method, 21 is split by 14. The matching divisor (7) as soon as remainder equates to 0 is taken together GCF.

How to uncover the GCF the 14 and also 21 by element Factorization?

To find the GCF of 14 and 21, us will uncover the prime factorization of the provided numbers, i.e. 14 = 2 × 7; 21 = 3 × 7.⇒ due to the fact that 7 is the only usual prime element of 14 and also 21. Hence, GCF (14, 21) = 7.☛ element Number