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GCF of 28 and 84

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

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

What is GCF of 28 and 84?

Answer: GCF of 28 and 84 is 28.

Explanation:

The GCF of two non-zero integers, x(28) and y(84), is the greatest positive integer m(28) that divides both x(28) and y(84) without any remainder.

Methods to Find GCF of 28 and 84

The methods to find the GCF of 28 and 84 are explained below.

Listing Common Factors
Using Euclid's Algorithm
Long Division Method

GCF of 28 and 84 by Listing Common Factors

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

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

GCF of 28 and 84 by Euclidean Algorithm

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

Here X = 84 and Y = 28

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

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

GCF of 28 and 84 by Long Division

GCF of 28 and 84 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 84 (larger number) by 28 (smaller number).
Step 2: Since the remainder = 0, the divisor (28) is the GCF of 28 and 84.

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

☛ Also Check:

GCF of 28 and 84 Examples

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

Solution:

Given: GCF = 28 and product of numbers = 2352
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 2352/28
Therefore, the LCM is 84.
Example 2: Find the GCF of 28 and 84, if their LCM is 84.

Solution:

∵ LCM × GCF = 28 × 84
⇒ GCF(28, 84) = (28 × 84)/84 = 28
Therefore, the greatest common factor of 28 and 84 is 28.
Example 3: Find the greatest number that divides 28 and 84 exactly.

Solution:

The greatest number that divides 28 and 84 exactly is their greatest common factor, i.e. GCF of 28 and 84.
⇒ Factors of 28 and 84:
- Factors of 28 = 1, 2, 4, 7, 14, 28
- Factors of 84 = 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Therefore, the GCF of 28 and 84 is 28.

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FAQs on GCF of 28 and 84

What is the GCF of 28 and 84?

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

What is the Relation Between LCM and GCF of 28, 84?

The following equation can be used to express the relation between LCM (Least Common Multiple) and GCF of 28 and 84, i.e. GCF × LCM = 28 × 84.

If the GCF of 84 and 28 is 28, Find its LCM.

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

How to Find the GCF of 28 and 84 by Long Division Method?

To find the GCF of 28, 84 using long division method, 84 is divided by 28. The corresponding divisor (28) when remainder equals 0 is taken as GCF.

How to Find the GCF of 28 and 84 by Prime Factorization?

To find the GCF of 28 and 84, we will find the prime factorization of the given numbers, i.e. 28 = 2 × 2 × 7; 84 = 2 × 2 × 3 × 7.
⇒ Since 2, 2, 7 are common terms in the prime factorization of 28 and 84. Hence, GCF(28, 84) = 2 × 2 × 7 = 28
☛ What is a Prime Number?

What are the Methods to Find GCF of 28 and 84?

There are three commonly used methods to find the GCF of 28 and 84.

By Long Division
By Prime Factorization
By Listing Common Factors

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