How to Find GCF of 289/216, 6141/9640?

GCF of 289/216, 6141/9640

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 289/216, 6141/9640 i.e 1/260280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 289/216, 6141/9640.

Enter two or more fractions separated by "commas"

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

What is the GCF of 289/216,6141/9640?

Given fractions are 289/216,6141/9640

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 289/216,6141/9640, numerators are 289,6141

Denominators are 216,9640

The GCF of 289,6141 is 1 .

LCM of 216,9640 is 260280.

The greatest common factor of 289/216,6141/9640 = [GCF of 289,6141]/[LCM of 216,9640]= 1/260280

Therefore, the GCF of 289/216,6141/9640 is 1/260280.

Greatest Common Factor of 289,6141

To find the highest common factor of 289,6141, 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 6141 are 1, 3, 23, 69, 89, 267, 2047, 6141

The HCF of 289,6141 is 1.

Lets's calculate GCF of 289,6141

Greatest Common Factor (GCF) of 289,6141 By Common Division

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

Greatest Common Factor of 289,6141 By Matching Biggest Common Factor Method

Now, list down the factors of 289

1,17,289

Now, list down the factors of 6141

1,3,23,69,89,267,2047,6141

Greatest Common Factor

We found the factors 289,6141 . The biggest common factor number is the GCF number.
So the greatest common factor 289,6141 is 1.

Lets's calculate LCM of 216,9640

Lowest Common Multiple of 216,9640 using Common Division

2	216, 9640
2	108, 4820
2	54, 2410
	27, 1205

∴ So the LCM of the given numbers is 2 x 2 x 2 x 27 x 1205 = 260280

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/260280

Therefore, the GCF of Fractions 289/216,6141/9640 is 1/260280

Least Common Multiple of 216,9640 with GCF Formula

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

We need to calculate greatest common factor of 216,9640 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(216,9640) = 8

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

GCF(216,9640) x common factors =8 x 1 = 8

LCM(216,9640) = ( 216 × 9640 ) / 8

LCM(216,9640) = 2082240 / 8

LCM(216,9640) = 260280

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FAQs on GCF of Fractions of 289/216, 6141/9640

1. What is the HCF of 289,6141?

The HCF of 289,6141 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 289/216, 6141/9640?

Answer: GCF of Numerators as per given numbers 289/216, 6141/9640 is

GCF of Numerators i.e. for 289,6141 is 1

LCM of denominators i.e. for 216,9640 is 260280.

Thus, GCF of Fractions is 1/260280.Finally, GCF of Fractions for 289/216, 6141/9640 is 1/260280.