GCF of 7 and 8 is the largest possible number the divides 7 and also 8 specifically without any remainder. The factors of 7 and also 8 room 1, 7 and also 1, 2, 4, 8 respectively. There space 3 frequently used methods to find the GCF that 7 and also 8 - long division, Euclidean algorithm, and also prime factorization.

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1.GCF that 7 and 8
2.List of Methods
3.Solved Examples
4.FAQs

Answer: GCF of 7 and also 8 is 1.

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Explanation:

The GCF of 2 non-zero integers, x(7) and also y(8), is the greatest positive essence m(1) that divides both x(7) and y(8) without any type of remainder.


The techniques to find the GCF that 7 and 8 are defined below.

Long department MethodUsing Euclid's AlgorithmListing typical Factors

GCF the 7 and 8 by long Division

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GCF the 7 and also 8 is the divisor the we acquire when the remainder becomes 0 ~ doing long department repeatedly.

Step 2: since the remainder ≠ 0, we will divide the divisor of action 1 (7) through the remainder (1).Step 3: Repeat this procedure until the remainder = 0.

The equivalent divisor (1) is the GCF the 7 and also 8.

GCF that 7 and also 8 through Euclidean Algorithm

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

Here X = 8 and also Y = 7

GCF(8, 7) = GCF(7, 8 mode 7) = GCF(7, 1)GCF(7, 1) = GCF(1, 7 mod 1) = GCF(1, 0)GCF(1, 0) = 1 (∵ GCF(X, 0) = |X|, wherein X ≠ 0)

Therefore, the value of GCF that 7 and 8 is 1.

GCF of 7 and 8 by Listing usual Factors

Factors of 7: 1, 7Factors of 8: 1, 2, 4, 8

Since, 1 is the only common factor in between 7 and also 8. The Greatest usual Factor of 7 and also 8 is 1.

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GCF that 7 and 8 Examples


Example 1: discover the biggest number that divides 7 and also 8 exactly.

Solution:

The biggest number that divides 7 and 8 precisely is their greatest typical factor, i.e. GCF of 7 and also 8.⇒ determinants of 7 and 8:

Factors of 7 = 1, 7Factors of 8 = 1, 2, 4, 8

Therefore, the GCF that 7 and also 8 is 1.


Example 2: discover the GCF the 7 and 8, if your LCM is 56.

Solution:

∵ LCM × GCF = 7 × 8⇒ GCF(7, 8) = (7 × 8)/56 = 1Therefore, the greatest common factor of 7 and 8 is 1.


Example 3: For two numbers, GCF = 1 and LCM = 56. If one number is 7, find the various other number.

Solution:

Given: GCF (z, 7) = 1 and also LCM (z, 7) = 56∵ GCF × LCM = 7 × (z)⇒ z = (GCF × LCM)/7⇒ z = (1 × 56)/7⇒ z = 8Therefore, the various other number is 8.


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FAQs top top GCF that 7 and 8

What is the GCF that 7 and 8?

The GCF of 7 and also 8 is 1. To calculate the greatest common factor (GCF) the 7 and also 8, we need to aspect each number (factors that 7 = 1, 7; determinants of 8 = 1, 2, 4, 8) and also choose the greatest element that precisely divides both 7 and also 8, i.e., 1.

How to uncover the GCF of 7 and 8 by Long department Method?

To uncover the GCF of 7, 8 making use of long division method, 8 is separated by 7. The equivalent divisor (1) once remainder amounts to 0 is taken as GCF.

What are the approaches to discover GCF the 7 and also 8?

There space three typically used methods to discover the GCF of 7 and 8.

By Euclidean AlgorithmBy element FactorizationBy lengthy Division

What is the Relation between LCM and also GCF the 7, 8?

The complying with equation can be used to refer the relation between LCM (Least typical Multiple) and GCF of 7 and 8, i.e. GCF × LCM = 7 × 8.

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How to uncover the GCF that 7 and 8 by element Factorization?

To find the GCF that 7 and 8, we will uncover the prime factorization of the given numbers, i.e. 7 = 7; 8 = 2 × 2 × 2.⇒ over there is no typical prime element for 7 and also 8. Hence, GCF (7, 8) = 1.☛ element Number

If the GCF the 8 and also 7 is 1, discover its LCM.

GCF(8, 7) × LCM(8, 7) = 8 × 7Since the GCF the 8 and also 7 = 1⇒ 1 × LCM(8, 7) = 56Therefore, LCM = 56☛ Greatest usual Factor Calculator