GCF that 21 and 84 is the largest feasible number the divides 21 and also 84 specifically without any remainder. The factors of 21 and 84 are 1, 3, 7, 21 and also 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 respectively. There are 3 generally used methods to find the GCF that 21 and 84 - Euclidean algorithm, prime factorization, and also long division.

You are watching: What is the greatest common factor of 21 and 84

1.GCF that 21 and also 84
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF the 21 and 84 is 21.

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Explanation:

The GCF of 2 non-zero integers, x(21) and y(84), is the greatest positive creature m(21) that divides both x(21) and also y(84) without any type of remainder.


The techniques to find the GCF of 21 and 84 are defined below.

Using Euclid's AlgorithmPrime administer MethodListing usual Factors

GCF of 21 and 84 by Euclidean Algorithm

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

Here X = 84 and also Y = 21

GCF(84, 21) = GCF(21, 84 mod 21) = GCF(21, 0)GCF(21, 0) = 21 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the worth of GCF of 21 and also 84 is 21.

GCF of 21 and also 84 by prime Factorization

Prime administer of 21 and also 84 is (3 × 7) and (2 × 2 × 3 × 7) respectively. Together visible, 21 and also 84 have usual prime factors. Hence, the GCF of 21 and 84 is 3 × 7 = 21.

GCF the 21 and also 84 through Listing typical Factors

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Factors the 21: 1, 3, 7, 21Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

There space 4 common factors the 21 and also 84, that are 1, 3, 21, and also 7. Therefore, the greatest common factor of 21 and also 84 is 21.

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GCF the 21 and also 84 Examples


Example 1: find the greatest number that divides 21 and also 84 exactly.

Solution:

The best number that divides 21 and 84 specifically is their greatest typical factor, i.e. GCF that 21 and 84.⇒ factors of 21 and also 84:

Factors of 21 = 1, 3, 7, 21Factors that 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

Therefore, the GCF that 21 and 84 is 21.


Example 2: For two numbers, GCF = 21 and also LCM = 84. If one number is 84, uncover the other number.

Solution:

Given: GCF (z, 84) = 21 and LCM (z, 84) = 84∵ GCF × LCM = 84 × (z)⇒ z = (GCF × LCM)/84⇒ z = (21 × 84)/84⇒ z = 21Therefore, the various other number is 21.


Example 3: The product of two numbers is 1764. If your GCF is 21, what is your LCM?

Solution:

Given: GCF = 21 and also product of number = 1764∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 1764/21Therefore, the LCM is 84.


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FAQs ~ above GCF that 21 and also 84

What is the GCF the 21 and also 84?

The GCF the 21 and also 84 is 21. To calculation the greatest common factor of 21 and also 84, we need to aspect each number (factors of 21 = 1, 3, 7, 21; determinants of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84) and also choose the greatest element that precisely divides both 21 and also 84, i.e., 21.

What space the techniques to uncover GCF that 21 and also 84?

There are three generally used techniques to discover the GCF of 21 and 84.

By prime FactorizationBy Euclidean AlgorithmBy lengthy Division

How to discover the GCF of 21 and 84 by element Factorization?

To discover the GCF of 21 and 84, we will find the prime factorization that the offered numbers, i.e. 21 = 3 × 7; 84 = 2 × 2 × 3 × 7.⇒ due to the fact that 3, 7 are common terms in the prime factorization of 21 and also 84. Hence, GCF(21, 84) = 3 × 7 = 21☛ What is a element Number?

What is the Relation in between LCM and also GCF the 21, 84?

The adhering to equation have the right to be supplied to express the relation in between Least common Multiple (LCM) and also GCF that 21 and 84, i.e. GCF × LCM = 21 × 84.

How to discover the GCF that 21 and also 84 through Long division Method?

To find the GCF of 21, 84 making use of long department method, 84 is separated by 21. The corresponding divisor (21) as soon as remainder equates to 0 is taken together GCF.

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If the GCF of 84 and 21 is 21, discover its LCM.

GCF(84, 21) × LCM(84, 21) = 84 × 21Since the GCF the 84 and also 21 = 21⇒ 21 × LCM(84, 21) = 1764Therefore, LCM = 84☛ Greatest usual Factor Calculator