How to Find GCF of 7678/469, 2178/5338?

GCF of 7678/469, 2178/5338

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 7678/469, 2178/5338 i.e 22/2503522 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7678/469, 2178/5338.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 7678/469,2178/5338?

Given fractions are 7678/469,2178/5338

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 7678/469,2178/5338, numerators are 7678,2178

Denominators are 469,5338

The GCF of 7678,2178 is 22 .

LCM of 469,5338 is 2503522.

The greatest common factor of 7678/469,2178/5338 = [GCF of 7678,2178]/[LCM of 469,5338]= 22/2503522

Therefore, the GCF of 7678/469,2178/5338 is 22/2503522.

Greatest Common Factor of 7678,2178

To find the highest common factor of 7678,2178, we have to find the factors of both numbers and list the highest common factor.

The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678

The factors of 2178 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 121, 198, 242, 363, 726, 1089, 2178

The HCF of 7678,2178 is 22.

Lets's calculate GCF of 7678,2178

Greatest Common Factor (GCF) of 7678,2178 By Common Division

2	7678, 2178
11	3839, 1089
	349, 99

∴ So the GCF of the given numbers is 2 x 11 = 22

Greatest Common Factor of 7678,2178 By Matching Biggest Common Factor Method

Now, list down the factors of 7678

1,2,11,22,349,698,3839,7678

Now, list down the factors of 2178

1,2,3,6,9,11,18,22,33,66,99,121,198,242,363,726,1089,2178

Greatest Common Factor

We found the factors 7678,2178 . The biggest common factor number is the GCF number.
So the greatest common factor 7678,2178 is 22.

Lets's calculate LCM of 469,5338

Lowest Common Multiple of 469,5338 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2503522

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/2503522

Therefore, the GCF of Fractions 7678/469,2178/5338 is 22/2503522

Least Common Multiple of 469,5338 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 469,5338 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(469,5338) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(469,5338) x common factors =1 x 1 = 1

LCM(469,5338) = ( 469 × 5338 ) / 1

LCM(469,5338) = 2503522 / 1

LCM(469,5338) = 2503522

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 7678/469, 2178/5338

1. What is the HCF of 7678,2178?

The HCF of 7678,2178 is 22

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 7678/469, 2178/5338?

Answer: GCF of Numerators as per given numbers 7678/469, 2178/5338 is

GCF of Numerators i.e. for 7678,2178 is 22

LCM of denominators i.e. for 469,5338 is 2503522.

Thus, GCF of Fractions is 22/2503522.Finally, GCF of Fractions for 7678/469, 2178/5338 is 22/2503522.