How to Find GCF of 26/275, 310/714, 676/298?

GCF of 26/275, 310/714, 676/298

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 26/275, 310/714, 676/298 i.e 2/29256150 easily. The following is the detailed procedure to determine the greatest common factor of fractions 26/275, 310/714, 676/298.

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 26/275,310/714,676/298?

Given fractions are 26/275,310/714,676/298

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 26/275,310/714,676/298, numerators are 26,310,676

Denominators are 275,714,298

The GCF of 26,310,676 is 2 .

LCM of 275,714,298 is 29256150.

The greatest common factor of 26/275,310/714,676/298 = [GCF of 26,310,676]/[LCM of 275,714,298]= 2/29256150

Therefore, the GCF of 26/275,310/714,676/298 is 2/29256150.

Greatest Common Factor of 26,310,676

To find the highest common factor of 26,310,676, we have to find the factors of both numbers and list the highest common factor.

The factors of 26 are 1, 2, 13, 26

The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310

The factors of 676 are 1, 2, 4, 13, 26, 52, 169, 338, 676

The HCF of 26,310,676 is 2.

Lets's calculate GCF of 26,310,676

Greatest Common Factor (GCF) of 26,310,676 By Common Division

2	26, 310, 676
	13, 155, 338

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 26,310,676 By Matching Biggest Common Factor Method

Now, list down the factors of 26

1,2,13,26

Now, list down the factors of 310

1,2,5,10,31,62,155,310

Now, list down the factors of 676

1,2,4,13,26,52,169,338,676

Greatest Common Factor

We found the factors 26,310,676 . The biggest common factor number is the GCF number.
So the greatest common factor 26,310,676 is 2.

Lets's calculate LCM of 275,714,298

Lowest Common Multiple of 275,714,298 using Common Division

2	275, 714, 298
	275, 357, 149

∴ So the LCM of the given numbers is 2 x 275 x 357 x 149 = 29256150

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/29256150

Therefore, the GCF of Fractions 26/275,310/714,676/298 is 2/29256150

Least Common Multiple of 275,714,298 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 275,714,298 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(275,714,298) = 1

common factors(in case of two or more numbers have common factors) = 2

GCF(275,714,298) x common factors =1 x 2 = 2

LCM(275,714,298) = ( 275 × 714 × 298 ) / 2

LCM(275,714,298) = 58512300 / 2

LCM(275,714,298) = 29256150

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 26/275, 310/714, 676/298

1. What is the HCF of 26,310,676?

The HCF of 26,310,676 is 2

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 26/275, 310/714, 676/298?

Answer: GCF of Numerators as per given numbers 26/275, 310/714, 676/298 is

GCF of Numerators i.e. for 26,310,676 is 2

LCM of denominators i.e. for 275,714,298 is 29256150.

Thus, GCF of Fractions is 2/29256150.Finally, GCF of Fractions for 26/275, 310/714, 676/298 is 2/29256150.