GCF of 28 and also 84 is the largest possible number that divides 28 and also 84 exactly without any remainder. The determinants of 28 and 84 space 1, 2, 4, 7, 14, 28 and also 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 respectively. There room 3 generally used approaches to uncover the GCF of 28 and 84 - long division, Euclidean algorithm, and prime factorization.

You are watching: What is the gcf of 28 and 84

1.GCF of 28 and 84
2.List the Methods
3.Solved Examples
4.FAQs

Answer: GCF of 28 and also 84 is 28.

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Explanation:

The GCF of 2 non-zero integers, x(28) and also y(84), is the best positive essence m(28) that divides both x(28) and y(84) without any kind of remainder.


The techniques to find the GCF that 28 and 84 are explained below.

Listing common FactorsUsing Euclid's AlgorithmLong department Method

GCF the 28 and also 84 by Listing common Factors

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

There room 6 usual factors that 28 and also 84, that are 1, 2, 4, 7, 14, and also 28. Therefore, the greatest typical factor of 28 and also 84 is 28.

GCF the 28 and also 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 = 28

GCF(84, 28) = GCF(28, 84 mode 28) = GCF(28, 0)GCF(28, 0) = 28 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the worth of GCF that 28 and also 84 is 28.

GCF of 28 and 84 by long Division

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GCF of 28 and 84 is the divisor the we gain when the remainder becomes 0 ~ doing long division repeatedly.

Step 2: due to the fact that the remainder = 0, the divisor (28) is the GCF the 28 and 84.

The equivalent divisor (28) is the GCF of 28 and 84.

☛ likewise Check:


GCF the 28 and 84 Examples


Example 1: The product of 2 numbers is 2352. If your GCF is 28, what is your LCM?

Solution:

Given: GCF = 28 and also product of numbers = 2352∵ LCM × GCF = product of numbers⇒ LCM = Product/GCF = 2352/28Therefore, the LCM is 84.


Example 2: discover the GCF of 28 and 84, if their LCM is 84.

Solution:

∵ LCM × GCF = 28 × 84⇒ GCF(28, 84) = (28 × 84)/84 = 28Therefore, the greatest typical factor the 28 and also 84 is 28.


Example 3: find the biggest number the divides 28 and also 84 exactly.

Solution:

The greatest number that divides 28 and 84 specifically is your greatest usual factor, i.e. GCF that 28 and 84.⇒ factors of 28 and 84:

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

Therefore, the GCF of 28 and also 84 is 28.


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FAQs on GCF that 28 and 84

What is the GCF that 28 and also 84?

The GCF that 28 and 84 is 28. To calculation the GCF of 28 and 84, we need to aspect each number (factors of 28 = 1, 2, 4, 7, 14, 28; 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 28 and 84, i.e., 28.

What is the Relation between LCM and also GCF that 28, 84?

The adhering to equation have the right to be offered to refer the relation in between LCM (Least typical Multiple) and GCF that 28 and also 84, i.e. GCF × LCM = 28 × 84.

If the GCF that 84 and also 28 is 28, find its LCM.

GCF(84, 28) × LCM(84, 28) = 84 × 28Since the GCF of 84 and 28 = 28⇒ 28 × LCM(84, 28) = 2352Therefore, LCM = 84☛ GCF Calculator

How to uncover the GCF the 28 and 84 by Long division Method?

To discover the GCF that 28, 84 using long division method, 84 is separated by 28. The corresponding divisor (28) when remainder amounts to 0 is taken as GCF.

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How to uncover the GCF of 28 and 84 by prime Factorization?

To uncover the GCF of 28 and 84, us will discover the element factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 84 = 2 × 2 × 3 × 7.⇒ due to the fact that 2, 2, 7 are usual terms in the prime factorization that 28 and also 84. Hence, GCF(28, 84) = 2 × 2 × 7 = 28☛ What is a element Number?

What are the methods to uncover GCF of 28 and 84?

There room three typically used methods to discover the GCF that 28 and 84.