How to Find GCF of 658/627, 1778/2294?

GCF of 658/627, 1778/2294

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 658/627, 1778/2294 i.e 14/1438338 easily. The following is the detailed procedure to determine the greatest common factor of fractions 658/627, 1778/2294.

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 658/627,1778/2294?

Given fractions are 658/627,1778/2294

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 658/627,1778/2294, numerators are 658,1778

Denominators are 627,2294

The GCF of 658,1778 is 14 .

LCM of 627,2294 is 1438338.

The greatest common factor of 658/627,1778/2294 = [GCF of 658,1778]/[LCM of 627,2294]= 14/1438338

Therefore, the GCF of 658/627,1778/2294 is 14/1438338.

Greatest Common Factor of 658,1778

To find the highest common factor of 658,1778, we have to find the factors of both numbers and list the highest common factor.

The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658

The factors of 1778 are 1, 2, 7, 14, 127, 254, 889, 1778

The HCF of 658,1778 is 14.

Lets's calculate GCF of 658,1778

Greatest Common Factor (GCF) of 658,1778 By Common Division

2	658, 1778
7	329, 889
	47, 127

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 658,1778 By Matching Biggest Common Factor Method

Now, list down the factors of 658

1,2,7,14,47,94,329,658

Now, list down the factors of 1778

1,2,7,14,127,254,889,1778

Greatest Common Factor

We found the factors 658,1778 . The biggest common factor number is the GCF number.
So the greatest common factor 658,1778 is 14.

Lets's calculate LCM of 627,2294

Lowest Common Multiple of 627,2294 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 1438338

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/1438338

Therefore, the GCF of Fractions 658/627,1778/2294 is 14/1438338

Least Common Multiple of 627,2294 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 627,2294 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(627,2294) = 1

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

GCF(627,2294) x common factors =1 x 1 = 1

LCM(627,2294) = ( 627 × 2294 ) / 1

LCM(627,2294) = 1438338 / 1

LCM(627,2294) = 1438338

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FAQs on GCF of Fractions of 658/627, 1778/2294

1. What is the HCF of 658,1778?

The HCF of 658,1778 is 14

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 658/627, 1778/2294?

Answer: GCF of Numerators as per given numbers 658/627, 1778/2294 is

GCF of Numerators i.e. for 658,1778 is 14

LCM of denominators i.e. for 627,2294 is 1438338.

Thus, GCF of Fractions is 14/1438338.Finally, GCF of Fractions for 658/627, 1778/2294 is 14/1438338.