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GCF of 257/35, 406/239

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 257/35, 406/239 i.e 1/8365 easily. The following is the detailed procedure to determine the greatest common factor of fractions 257/35, 406/239.

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 257/35,406/239?

Given fractions are 257/35,406/239

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 257/35,406/239, numerators are 257,406

Denominators are 35,239

The GCF of 257,406 is 1 .

LCM of 35,239 is 8365.

The greatest common factor of 257/35,406/239 = [GCF of 257,406]/[LCM of 35,239]= 1/8365

Therefore, the GCF of 257/35,406/239 is 1/8365.

Greatest Common Factor of 257,406

To find the highest common factor of 257,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 257 are 1, 257

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 257,406 is 1.

Lets's calculate GCF of 257,406

Greatest Common Factor (GCF) of 257,406 By Common Division

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

Greatest Common Factor of 257,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 257,406 By Matching Biggest Common Factor Method

Now, list down the factors of 257

:

1,257

Now, list down the factors of 406

:

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 257,406 . The biggest common factor number is the GCF number.
So the greatest common factor 257,406 is 1.

Lets's calculate LCM of 35,239

Lowest Common Multiple of 35,239 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 8365

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/8365

Therefore, the GCF of Fractions 257/35,406/239 is 1/8365

Least Common Multiple of 35,239 with GCF Formula

Least Common Multiple of 35,239 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 35,239 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(35,239) = 1

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

GCF(35,239) x common factors =1 x 1 = 1

LCM(35,239) = ( 35 × 239 ) / 1

LCM(35,239) = 8365 / 1

LCM(35,239) = 8365


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FAQs on GCF of Fractions of 257/35, 406/239

1. What is the HCF of 257,406?

The HCF of 257,406 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 257/35, 406/239?

Answer: GCF of Numerators as per given numbers 257/35, 406/239 is

GCF of Numerators i.e. for 257,406 is 1

LCM of denominators i.e. for 35,239 is 8365.

Thus, GCF of Fractions is 1/8365.Finally, GCF of Fractions for 257/35, 406/239 is 1/8365.