How to Find GCF of 76/80, 55/289, 659/404?

GCF of 76/80, 55/289, 659/404

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 76/80, 55/289, 659/404 i.e 1/2335120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 76/80, 55/289, 659/404.

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 76/80,55/289,659/404?

Given fractions are 76/80,55/289,659/404

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 76/80,55/289,659/404, numerators are 76,55,659

Denominators are 80,289,404

The GCF of 76,55,659 is 1 .

LCM of 80,289,404 is 2335120.

The greatest common factor of 76/80,55/289,659/404 = [GCF of 76,55,659]/[LCM of 80,289,404]= 1/2335120

Therefore, the GCF of 76/80,55/289,659/404 is 1/2335120.

Greatest Common Factor of 76,55,659

To find the highest common factor of 76,55,659, we have to find the factors of both numbers and list the highest common factor.

The factors of 76 are 1, 2, 4, 19, 38, 76

The factors of 55 are 1, 5, 11, 55

The factors of 659 are 1, 659

The HCF of 76,55,659 is 1.

Lets's calculate GCF of 76,55,659

Greatest Common Factor (GCF) of 76,55,659 By Common Division

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

Greatest Common Factor of 76,55,659 By Matching Biggest Common Factor Method

Now, list down the factors of 76

1,2,4,19,38,76

Now, list down the factors of 55

1,5,11,55

Now, list down the factors of 659

1,659

Greatest Common Factor

We found the factors 76,55,659 . The biggest common factor number is the GCF number.
So the greatest common factor 76,55,659 is 1.

Lets's calculate LCM of 80,289,404

Lowest Common Multiple of 80,289,404 using Common Division

2	80, 289, 404
2	40, 289, 202
	20, 289, 101

∴ So the LCM of the given numbers is 2 x 2 x 20 x 289 x 101 = 2335120

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2335120

Therefore, the GCF of Fractions 76/80,55/289,659/404 is 1/2335120

Least Common Multiple of 80,289,404 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 80,289,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(80,289,404) = 1

common factors(in case of two or more numbers have common factors) = 4

GCF(80,289,404) x common factors =1 x 4 = 4

LCM(80,289,404) = ( 80 × 289 × 404 ) / 4

LCM(80,289,404) = 9340480 / 4

LCM(80,289,404) = 2335120

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FAQs on GCF of Fractions of 76/80, 55/289, 659/404

1. What is the HCF of 76,55,659?

The HCF of 76,55,659 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 76/80, 55/289, 659/404?

Answer: GCF of Numerators as per given numbers 76/80, 55/289, 659/404 is

GCF of Numerators i.e. for 76,55,659 is 1

LCM of denominators i.e. for 80,289,404 is 2335120.

Thus, GCF of Fractions is 1/2335120.Finally, GCF of Fractions for 76/80, 55/289, 659/404 is 1/2335120.