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GCF of 289/16, 277/181

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 289/16, 277/181 i.e 1/2896 easily. The following is the detailed procedure to determine the greatest common factor of fractions 289/16, 277/181.

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 289/16,277/181?

Given fractions are 289/16,277/181

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 289/16,277/181, numerators are 289,277

Denominators are 16,181

The GCF of 289,277 is 1 .

LCM of 16,181 is 2896.

The greatest common factor of 289/16,277/181 = [GCF of 289,277]/[LCM of 16,181]= 1/2896

Therefore, the GCF of 289/16,277/181 is 1/2896.

Greatest Common Factor of 289,277

To find the highest common factor of 289,277, we have to find the factors of both numbers and list the highest common factor.

The factors of 289 are 1, 17, 289

The factors of 277 are 1, 277

The HCF of 289,277 is 1.

Lets's calculate GCF of 289,277

Greatest Common Factor (GCF) of 289,277 By Common Division

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

Greatest Common Factor of 289,277 By Matching Biggest Common Factor Method

Greatest Common Factor of 289,277 By Matching Biggest Common Factor Method

Now, list down the factors of 289

:

1,17,289

Now, list down the factors of 277

:

1,277

Greatest Common Factor

We found the factors 289,277 . The biggest common factor number is the GCF number.
So the greatest common factor 289,277 is 1.

Lets's calculate LCM of 16,181

Lowest Common Multiple of 16,181 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 2896

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2896

Therefore, the GCF of Fractions 289/16,277/181 is 1/2896

Least Common Multiple of 16,181 with GCF Formula

Least Common Multiple of 16,181 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 16,181 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(16,181) = 1

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

GCF(16,181) x common factors =1 x 1 = 1

LCM(16,181) = ( 16 × 181 ) / 1

LCM(16,181) = 2896 / 1

LCM(16,181) = 2896


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FAQs on GCF of Fractions of 289/16, 277/181

1. What is the HCF of 289,277?

The HCF of 289,277 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 289/16, 277/181?

Answer: GCF of Numerators as per given numbers 289/16, 277/181 is

GCF of Numerators i.e. for 289,277 is 1

LCM of denominators i.e. for 16,181 is 2896.

Thus, GCF of Fractions is 1/2896.Finally, GCF of Fractions for 289/16, 277/181 is 1/2896.