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GCF of 7 and 28

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

1.	GCF of 7 and 28
2.	List of Methods
3.	Solved Examples
4.	FAQs

What is GCF of 7 and 28?

Answer: GCF of 7 and 28 is 7.

Explanation:

The GCF of two non-zero integers, x(7) and y(28), is the greatest positive integer m(7) that divides both x(7) and y(28) without any remainder.

Methods to Find GCF of 7 and 28

Let's look at the different methods for finding the GCF of 7 and 28.

Long Division Method
Listing Common Factors
Using Euclid's Algorithm

GCF of 7 and 28 by Long Division

GCF of 7 and 28 is the divisor that we get when the remainder becomes 0 after doing long division repeatedly.

Step 1: Divide 28 (larger number) by 7 (smaller number).
Step 2: Since the remainder = 0, the divisor (7) is the GCF of 7 and 28.

The corresponding divisor (7) is the GCF of 7 and 28.

GCF of 7 and 28 by Listing Common Factors

Factors of 7: 1, 7
Factors of 28: 1, 2, 4, 7, 14, 28

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

GCF of 7 and 28 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 = 28 and Y = 7

GCF(28, 7) = GCF(7, 28 mod 7) = GCF(7, 0)
GCF(7, 0) = 7 (∵ GCF(X, 0) = |X|, where X ≠ 0)

Therefore, the value of GCF of 7 and 28 is 7.

☛ Also Check:

GCF of 7 and 28 Examples

Example 1: Find the greatest number that divides 7 and 28 exactly.

Solution:

The greatest number that divides 7 and 28 exactly is their greatest common factor, i.e. GCF of 7 and 28.
⇒ Factors of 7 and 28:
- Factors of 7 = 1, 7
- Factors of 28 = 1, 2, 4, 7, 14, 28
Therefore, the GCF of 7 and 28 is 7.
Example 2: The product of two numbers is 196. If their GCF is 7, what is their LCM?

Solution:

Given: GCF = 7 and product of numbers = 196
∵ LCM × GCF = product of numbers
⇒ LCM = Product/GCF = 196/7
Therefore, the LCM is 28.
Example 3: Find the GCF of 7 and 28, if their LCM is 28.

Solution:

∵ LCM × GCF = 7 × 28
⇒ GCF(7, 28) = (7 × 28)/28 = 7
Therefore, the greatest common factor of 7 and 28 is 7.

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FAQs on GCF of 7 and 28

What is the GCF of 7 and 28?

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

How to Find the GCF of 7 and 28 by Prime Factorization?

To find the GCF of 7 and 28, we will find the prime factorization of the given numbers, i.e. 7 = 7; 28 = 2 × 2 × 7.
⇒ Since 7 is the only common prime factor of 7 and 28. Hence, GCF (7, 28) = 7.
☛ Prime Number

If the GCF of 28 and 7 is 7, Find its LCM.

GCF(28, 7) × LCM(28, 7) = 28 × 7
Since the GCF of 28 and 7 = 7
⇒ 7 × LCM(28, 7) = 196
Therefore, LCM = 28
☛ Greatest Common Factor Calculator

What is the Relation Between LCM and GCF of 7, 28?

The following equation can be used to express the relation between Least Common Multiple (LCM) and GCF of 7 and 28, i.e. GCF × LCM = 7 × 28.

What are the Methods to Find GCF of 7 and 28?

There are three commonly used methods to find the GCF of 7 and 28.

By Euclidean Algorithm
By Prime Factorization
By Long Division

How to Find the GCF of 7 and 28 by Long Division Method?

To find the GCF of 7, 28 using long division method, 28 is divided by 7. The corresponding divisor (7) when remainder equals 0 is taken as GCF.

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