How to Find GCF of 270/766, 340/909?

GCF of 270/766, 340/909

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 270/766, 340/909 i.e 10/696294 easily. The following is the detailed procedure to determine the greatest common factor of fractions 270/766, 340/909.

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 270/766,340/909?

Given fractions are 270/766,340/909

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 270/766,340/909, numerators are 270,340

Denominators are 766,909

The GCF of 270,340 is 10 .

LCM of 766,909 is 696294.

The greatest common factor of 270/766,340/909 = [GCF of 270,340]/[LCM of 766,909]= 10/696294

Therefore, the GCF of 270/766,340/909 is 10/696294.

Greatest Common Factor of 270,340

To find the highest common factor of 270,340, we have to find the factors of both numbers and list the highest common factor.

The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270

The factors of 340 are 1, 2, 4, 5, 10, 17, 20, 34, 68, 85, 170, 340

The HCF of 270,340 is 10.

Lets's calculate GCF of 270,340

Greatest Common Factor (GCF) of 270,340 By Common Division

2	270, 340
5	135, 170
	27, 34

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 270,340 By Matching Biggest Common Factor Method

Now, list down the factors of 270

1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270

Now, list down the factors of 340

1,2,4,5,10,17,20,34,68,85,170,340

Greatest Common Factor

We found the factors 270,340 . The biggest common factor number is the GCF number.
So the greatest common factor 270,340 is 10.

Lets's calculate LCM of 766,909

Lowest Common Multiple of 766,909 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 696294

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/696294

Therefore, the GCF of Fractions 270/766,340/909 is 10/696294

Least Common Multiple of 766,909 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 766,909 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(766,909) = 1

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

GCF(766,909) x common factors =1 x 1 = 1

LCM(766,909) = ( 766 × 909 ) / 1

LCM(766,909) = 696294 / 1

LCM(766,909) = 696294

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FAQs on GCF of Fractions of 270/766, 340/909

1. What is the HCF of 270,340?

The HCF of 270,340 is 10

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 270/766, 340/909?

Answer: GCF of Numerators as per given numbers 270/766, 340/909 is

GCF of Numerators i.e. for 270,340 is 10

LCM of denominators i.e. for 766,909 is 696294.

Thus, GCF of Fractions is 10/696294.Finally, GCF of Fractions for 270/766, 340/909 is 10/696294.