How to Find GCF of 678/469, 7129/754?

GCF of 678/469, 7129/754

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 678/469, 7129/754 i.e 1/353626 easily. The following is the detailed procedure to determine the greatest common factor of fractions 678/469, 7129/754.

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 678/469,7129/754?

Given fractions are 678/469,7129/754

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 678/469,7129/754, numerators are 678,7129

Denominators are 469,754

The GCF of 678,7129 is 1 .

LCM of 469,754 is 353626.

The greatest common factor of 678/469,7129/754 = [GCF of 678,7129]/[LCM of 469,754]= 1/353626

Therefore, the GCF of 678/469,7129/754 is 1/353626.

Greatest Common Factor of 678,7129

To find the highest common factor of 678,7129, we have to find the factors of both numbers and list the highest common factor.

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

The factors of 7129 are 1, 7129

The HCF of 678,7129 is 1.

Lets's calculate GCF of 678,7129

Greatest Common Factor (GCF) of 678,7129 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 678,7129 By Matching Biggest Common Factor Method

Now, list down the factors of 678

1,2,3,6,113,226,339,678

Now, list down the factors of 7129

1,7129

Greatest Common Factor

We found the factors 678,7129 . The biggest common factor number is the GCF number.
So the greatest common factor 678,7129 is 1.

Lets's calculate LCM of 469,754

Lowest Common Multiple of 469,754 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 353626

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/353626

Therefore, the GCF of Fractions 678/469,7129/754 is 1/353626

Least Common Multiple of 469,754 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 469,754 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(469,754) = 1

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

GCF(469,754) x common factors =1 x 1 = 1

LCM(469,754) = ( 469 × 754 ) / 1

LCM(469,754) = 353626 / 1

LCM(469,754) = 353626

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FAQs on GCF of Fractions of 678/469, 7129/754

1. What is the HCF of 678,7129?

The HCF of 678,7129 is 1

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 678/469, 7129/754?

Answer: GCF of Numerators as per given numbers 678/469, 7129/754 is

GCF of Numerators i.e. for 678,7129 is 1

LCM of denominators i.e. for 469,754 is 353626.

Thus, GCF of Fractions is 1/353626.Finally, GCF of Fractions for 678/469, 7129/754 is 1/353626.