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GCF of 661/268, 289/270

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 661/268, 289/270 i.e 1/36180 easily. The following is the detailed procedure to determine the greatest common factor of fractions 661/268, 289/270.

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 661/268,289/270?

Given fractions are 661/268,289/270

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 661/268,289/270, numerators are 661,289

Denominators are 268,270

The GCF of 661,289 is 1 .

LCM of 268,270 is 36180.

The greatest common factor of 661/268,289/270 = [GCF of 661,289]/[LCM of 268,270]= 1/36180

Therefore, the GCF of 661/268,289/270 is 1/36180.

Greatest Common Factor of 661,289

To find the highest common factor of 661,289, we have to find the factors of both numbers and list the highest common factor.

The factors of 661 are 1, 661

The factors of 289 are 1, 17, 289

The HCF of 661,289 is 1.

Lets's calculate GCF of 661,289

Greatest Common Factor (GCF) of 661,289 By Common Division

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

Greatest Common Factor of 661,289 By Matching Biggest Common Factor Method

Greatest Common Factor of 661,289 By Matching Biggest Common Factor Method

Now, list down the factors of 661

:

1,661

Now, list down the factors of 289

:

1,17,289

Greatest Common Factor

We found the factors 661,289 . The biggest common factor number is the GCF number.
So the greatest common factor 661,289 is 1.

Lets's calculate LCM of 268,270

Lowest Common Multiple of 268,270 using Common Division

2 268, 270
134, 135

∴ So the LCM of the given numbers is 2 x 134 x 135 = 36180

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/36180

Therefore, the GCF of Fractions 661/268,289/270 is 1/36180

Least Common Multiple of 268,270 with GCF Formula

Least Common Multiple of 268,270 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 268,270 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(268,270) = 2

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

GCF(268,270) x common factors =2 x 1 = 2

LCM(268,270) = ( 268 × 270 ) / 2

LCM(268,270) = 72360 / 2

LCM(268,270) = 36180


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FAQs on GCF of Fractions of 661/268, 289/270

1. What is the HCF of 661,289?

The HCF of 661,289 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 661/268, 289/270?

Answer: GCF of Numerators as per given numbers 661/268, 289/270 is

GCF of Numerators i.e. for 661,289 is 1

LCM of denominators i.e. for 268,270 is 36180.

Thus, GCF of Fractions is 1/36180.Finally, GCF of Fractions for 661/268, 289/270 is 1/36180.