How to Find GCF of 870/842, 710/591?

GCF of 870/842, 710/591

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 870/842, 710/591 i.e 10/497622 easily. The following is the detailed procedure to determine the greatest common factor of fractions 870/842, 710/591.

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 870/842,710/591?

Given fractions are 870/842,710/591

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 870/842,710/591, numerators are 870,710

Denominators are 842,591

The GCF of 870,710 is 10 .

LCM of 842,591 is 497622.

The greatest common factor of 870/842,710/591 = [GCF of 870,710]/[LCM of 842,591]= 10/497622

Therefore, the GCF of 870/842,710/591 is 10/497622.

Greatest Common Factor of 870,710

To find the highest common factor of 870,710, we have to find the factors of both numbers and list the highest common factor.

The factors of 870 are 1, 2, 3, 5, 6, 10, 15, 29, 30, 58, 87, 145, 174, 290, 435, 870

The factors of 710 are 1, 2, 5, 10, 71, 142, 355, 710

The HCF of 870,710 is 10.

Lets's calculate GCF of 870,710

Greatest Common Factor (GCF) of 870,710 By Common Division

2	870, 710
5	435, 355
	87, 71

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

Greatest Common Factor of 870,710 By Matching Biggest Common Factor Method

Now, list down the factors of 870

1,2,3,5,6,10,15,29,30,58,87,145,174,290,435,870

Now, list down the factors of 710

1,2,5,10,71,142,355,710

Greatest Common Factor

We found the factors 870,710 . The biggest common factor number is the GCF number.
So the greatest common factor 870,710 is 10.

Lets's calculate LCM of 842,591

Lowest Common Multiple of 842,591 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 497622

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/497622

Therefore, the GCF of Fractions 870/842,710/591 is 10/497622

Least Common Multiple of 842,591 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 842,591 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(842,591) = 1

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

GCF(842,591) x common factors =1 x 1 = 1

LCM(842,591) = ( 842 × 591 ) / 1

LCM(842,591) = 497622 / 1

LCM(842,591) = 497622

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FAQs on GCF of Fractions of 870/842, 710/591

1. What is the HCF of 870,710?

The HCF of 870,710 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 870/842, 710/591?

Answer: GCF of Numerators as per given numbers 870/842, 710/591 is

GCF of Numerators i.e. for 870,710 is 10

LCM of denominators i.e. for 842,591 is 497622.

Thus, GCF of Fractions is 10/497622.Finally, GCF of Fractions for 870/842, 710/591 is 10/497622.