GCF the 7 and 28 is the largest possible number the divides 7 and 28 precisely without any kind of remainder. The factors of 7 and 28 room 1, 7 and 1, 2, 4, 7, 14, 28 respectively. There are 3 typically used techniques to discover the GCF the 7 and also 28 - Euclidean algorithm, lengthy division, and prime factorization.

You are watching: What is the greatest common factor of 7 and 28

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

Answer: GCF that 7 and 28 is 7.

Explanation:

The GCF of 2 non-zero integers, x(7) and y(28), is the biggest positive integer m(7) that divides both x(7) and also y(28) without any remainder.

Let's look in ~ the various methods because that finding the GCF of 7 and also 28.

Long department MethodListing common FactorsUsing Euclid's Algorithm

### GCF that 7 and also 28 by lengthy Division

GCF the 7 and also 28 is the divisor the we acquire when the remainder becomes 0 after ~ doing long division repeatedly.

Step 2: since the remainder = 0, the divisor (7) is the GCF the 7 and also 28.

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

### GCF that 7 and also 28 through Listing typical Factors

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

There space 2 common factors that 7 and 28, that space 1 and also 7. Therefore, the greatest common factor that 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 also mod is the modulo operator.

Here X = 28 and also Y = 7

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

Therefore, the worth of GCF of 7 and also 28 is 7.

☛ also Check:

## GCF of 7 and also 28 Examples

Example 1: discover the greatest number the divides 7 and also 28 exactly.

Solution:

The greatest number the divides 7 and also 28 specifically is their greatest usual factor, i.e. GCF of 7 and also 28.⇒ factors of 7 and 28:

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

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

Example 2: The product of 2 numbers is 196. If their GCF is 7, what is your LCM?

Solution:

Given: GCF = 7 and product of number = 196∵ LCM × GCF = product the numbers⇒ LCM = Product/GCF = 196/7Therefore, the LCM is 28.

Example 3: find the GCF that 7 and 28, if your LCM is 28.

Solution:

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

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## FAQs ~ above GCF that 7 and 28

### What is the GCF that 7 and also 28?

The GCF of 7 and also 28 is 7. To calculation the GCF that 7 and also 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 aspect that specifically divides both 7 and 28, i.e., 7.

### How to uncover the GCF of 7 and 28 by element Factorization?

To discover the GCF of 7 and 28, we will find the prime factorization the the given numbers, i.e. 7 = 7; 28 = 2 × 2 × 7.⇒ since 7 is the only usual prime aspect of 7 and also 28. Hence, GCF (7, 28) = 7.☛ element Number

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

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

### What is the Relation between LCM and also GCF that 7, 28?

The following equation deserve to be used to express the relation between Least common Multiple (LCM) and also GCF that 7 and 28, i.e. GCF × LCM = 7 × 28.

### What space the methods to uncover GCF that 7 and also 28?

There space three frequently used approaches to uncover the GCF that 7 and also 28.

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By Euclidean AlgorithmBy element FactorizationBy lengthy Division

### How to uncover the GCF the 7 and 28 by Long division Method?

To uncover the GCF the 7, 28 using long department method, 28 is separated by 7. The matching divisor (7) as soon as remainder equates to 0 is taken as GCF.