How to Find GCF of 838/268, 870/356?

GCF of 838/268, 870/356

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 838/268, 870/356 i.e 2/23852 easily. The following is the detailed procedure to determine the greatest common factor of fractions 838/268, 870/356.

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 838/268,870/356?

Given fractions are 838/268,870/356

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 838/268,870/356, numerators are 838,870

Denominators are 268,356

The GCF of 838,870 is 2 .

LCM of 268,356 is 23852.

The greatest common factor of 838/268,870/356 = [GCF of 838,870]/[LCM of 268,356]= 2/23852

Therefore, the GCF of 838/268,870/356 is 2/23852.

Greatest Common Factor of 838,870

To find the highest common factor of 838,870, we have to find the factors of both numbers and list the highest common factor.

The factors of 838 are 1, 2, 419, 838

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

The HCF of 838,870 is 2.

Lets's calculate GCF of 838,870

Greatest Common Factor (GCF) of 838,870 By Common Division

2	838, 870
	419, 435

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

Greatest Common Factor of 838,870 By Matching Biggest Common Factor Method

Now, list down the factors of 838

1,2,419,838

Now, list down the factors of 870

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

Greatest Common Factor

We found the factors 838,870 . The biggest common factor number is the GCF number.
So the greatest common factor 838,870 is 2.

Lets's calculate LCM of 268,356

Lowest Common Multiple of 268,356 using Common Division

2	268, 356
2	134, 178
	67, 89

∴ So the LCM of the given numbers is 2 x 2 x 67 x 89 = 23852

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/23852

Therefore, the GCF of Fractions 838/268,870/356 is 2/23852

Least Common Multiple of 268,356 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 268,356 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(268,356) = 4

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

GCF(268,356) x common factors =4 x 1 = 4

LCM(268,356) = ( 268 × 356 ) / 4

LCM(268,356) = 95408 / 4

LCM(268,356) = 23852

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FAQs on GCF of Fractions of 838/268, 870/356

1. What is the HCF of 838,870?

The HCF of 838,870 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 838/268, 870/356?

Answer: GCF of Numerators as per given numbers 838/268, 870/356 is

GCF of Numerators i.e. for 838,870 is 2

LCM of denominators i.e. for 268,356 is 23852.

Thus, GCF of Fractions is 2/23852.Finally, GCF of Fractions for 838/268, 870/356 is 2/23852.