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GCF of 140/270, 653/298

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 140/270, 653/298 i.e 1/40230 easily. The following is the detailed procedure to determine the greatest common factor of fractions 140/270, 653/298.

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 140/270,653/298?

Given fractions are 140/270,653/298

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 140/270,653/298, numerators are 140,653

Denominators are 270,298

The GCF of 140,653 is 1 .

LCM of 270,298 is 40230.

The greatest common factor of 140/270,653/298 = [GCF of 140,653]/[LCM of 270,298]= 1/40230

Therefore, the GCF of 140/270,653/298 is 1/40230.

Greatest Common Factor of 140,653

To find the highest common factor of 140,653, we have to find the factors of both numbers and list the highest common factor.

The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140

The factors of 653 are 1, 653

The HCF of 140,653 is 1.

Lets's calculate GCF of 140,653

Greatest Common Factor (GCF) of 140,653 By Common Division

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

Greatest Common Factor of 140,653 By Matching Biggest Common Factor Method

Greatest Common Factor of 140,653 By Matching Biggest Common Factor Method

Now, list down the factors of 140

:

1,2,4,5,7,10,14,20,28,35,70,140

Now, list down the factors of 653

:

1,653

Greatest Common Factor

We found the factors 140,653 . The biggest common factor number is the GCF number.
So the greatest common factor 140,653 is 1.

Lets's calculate LCM of 270,298

Lowest Common Multiple of 270,298 using Common Division

2 270, 298
135, 149

∴ So the LCM of the given numbers is 2 x 135 x 149 = 40230

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/40230

Therefore, the GCF of Fractions 140/270,653/298 is 1/40230

Least Common Multiple of 270,298 with GCF Formula

Least Common Multiple of 270,298 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 270,298 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(270,298) = 2

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

GCF(270,298) x common factors =2 x 1 = 2

LCM(270,298) = ( 270 × 298 ) / 2

LCM(270,298) = 80460 / 2

LCM(270,298) = 40230


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FAQs on GCF of Fractions of 140/270, 653/298

1. What is the HCF of 140,653?

The HCF of 140,653 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 140/270, 653/298?

Answer: GCF of Numerators as per given numbers 140/270, 653/298 is

GCF of Numerators i.e. for 140,653 is 1

LCM of denominators i.e. for 270,298 is 40230.

Thus, GCF of Fractions is 1/40230.Finally, GCF of Fractions for 140/270, 653/298 is 1/40230.