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GCF of 419/975, 257/564

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 419/975, 257/564 i.e 1/183300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 419/975, 257/564.

Enter two or more fractions separated by "commas"

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

GCF of:

What is the GCF of 419/975,257/564?

Given fractions are 419/975,257/564

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 419/975,257/564, numerators are 419,257

Denominators are 975,564

The GCF of 419,257 is 1 .

LCM of 975,564 is 183300.

The greatest common factor of 419/975,257/564 = [GCF of 419,257]/[LCM of 975,564]= 1/183300

Therefore, the GCF of 419/975,257/564 is 1/183300.

Greatest Common Factor of 419,257

To find the highest common factor of 419,257, we have to find the factors of both numbers and list the highest common factor.

The factors of 419 are 1, 419

The factors of 257 are 1, 257

The HCF of 419,257 is 1.

Lets's calculate GCF of 419,257

Greatest Common Factor (GCF) of 419,257 By Common Division

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

Greatest Common Factor of 419,257 By Matching Biggest Common Factor Method

Greatest Common Factor of 419,257 By Matching Biggest Common Factor Method

Now, list down the factors of 419

:

1,419

Now, list down the factors of 257

:

1,257

Greatest Common Factor

We found the factors 419,257 . The biggest common factor number is the GCF number.
So the greatest common factor 419,257 is 1.

Lets's calculate LCM of 975,564

Lowest Common Multiple of 975,564 using Common Division

3 975, 564
325, 188

∴ So the LCM of the given numbers is 3 x 325 x 188 = 183300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/183300

Therefore, the GCF of Fractions 419/975,257/564 is 1/183300

Least Common Multiple of 975,564 with GCF Formula

Least Common Multiple of 975,564 with GCF Formula

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

We need to calculate greatest common factor of 975,564 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(975,564) = 3

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

GCF(975,564) x common factors =3 x 1 = 3

LCM(975,564) = ( 975 × 564 ) / 3

LCM(975,564) = 549900 / 3

LCM(975,564) = 183300


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FAQs on GCF of Fractions of 419/975, 257/564

1. What is the HCF of 419,257?

The HCF of 419,257 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 419/975, 257/564?

Answer: GCF of Numerators as per given numbers 419/975, 257/564 is

GCF of Numerators i.e. for 419,257 is 1

LCM of denominators i.e. for 975,564 is 183300.

Thus, GCF of Fractions is 1/183300.Finally, GCF of Fractions for 419/975, 257/564 is 1/183300.