How to Find GCF of 538/364, 1057/619?

GCF of 538/364, 1057/619

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 538/364, 1057/619 i.e 1/225316 easily. The following is the detailed procedure to determine the greatest common factor of fractions 538/364, 1057/619.

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 538/364,1057/619?

Given fractions are 538/364,1057/619

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 538/364,1057/619, numerators are 538,1057

Denominators are 364,619

The GCF of 538,1057 is 1 .

LCM of 364,619 is 225316.

The greatest common factor of 538/364,1057/619 = [GCF of 538,1057]/[LCM of 364,619]= 1/225316

Therefore, the GCF of 538/364,1057/619 is 1/225316.

Greatest Common Factor of 538,1057

To find the highest common factor of 538,1057, we have to find the factors of both numbers and list the highest common factor.

The factors of 538 are 1, 2, 269, 538

The factors of 1057 are 1, 7, 151, 1057

The HCF of 538,1057 is 1.

Lets's calculate GCF of 538,1057

Greatest Common Factor (GCF) of 538,1057 By Common Division

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

Greatest Common Factor of 538,1057 By Matching Biggest Common Factor Method

Now, list down the factors of 538

1,2,269,538

Now, list down the factors of 1057

1,7,151,1057

Greatest Common Factor

We found the factors 538,1057 . The biggest common factor number is the GCF number.
So the greatest common factor 538,1057 is 1.

Lets's calculate LCM of 364,619

Lowest Common Multiple of 364,619 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 225316

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/225316

Therefore, the GCF of Fractions 538/364,1057/619 is 1/225316

Least Common Multiple of 364,619 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 364,619 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(364,619) = 1

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

GCF(364,619) x common factors =1 x 1 = 1

LCM(364,619) = ( 364 × 619 ) / 1

LCM(364,619) = 225316 / 1

LCM(364,619) = 225316

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FAQs on GCF of Fractions of 538/364, 1057/619

1. What is the HCF of 538,1057?

The HCF of 538,1057 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 538/364, 1057/619?

Answer: GCF of Numerators as per given numbers 538/364, 1057/619 is

GCF of Numerators i.e. for 538,1057 is 1

LCM of denominators i.e. for 364,619 is 225316.

Thus, GCF of Fractions is 1/225316.Finally, GCF of Fractions for 538/364, 1057/619 is 1/225316.