How to Find GCF of 874/268, 2710/820?

GCF of 874/268, 2710/820

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 874/268, 2710/820 i.e 2/54940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 874/268, 2710/820.

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 874/268,2710/820?

Given fractions are 874/268,2710/820

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 874/268,2710/820, numerators are 874,2710

Denominators are 268,820

The GCF of 874,2710 is 2 .

LCM of 268,820 is 54940.

The greatest common factor of 874/268,2710/820 = [GCF of 874,2710]/[LCM of 268,820]= 2/54940

Therefore, the GCF of 874/268,2710/820 is 2/54940.

Greatest Common Factor of 874,2710

To find the highest common factor of 874,2710, we have to find the factors of both numbers and list the highest common factor.

The factors of 874 are 1, 2, 19, 23, 38, 46, 437, 874

The factors of 2710 are 1, 2, 5, 10, 271, 542, 1355, 2710

The HCF of 874,2710 is 2.

Lets's calculate GCF of 874,2710

Greatest Common Factor (GCF) of 874,2710 By Common Division

2	874, 2710
	437, 1355

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

Greatest Common Factor of 874,2710 By Matching Biggest Common Factor Method

Now, list down the factors of 874

1,2,19,23,38,46,437,874

Now, list down the factors of 2710

1,2,5,10,271,542,1355,2710

Greatest Common Factor

We found the factors 874,2710 . The biggest common factor number is the GCF number.
So the greatest common factor 874,2710 is 2.

Lets's calculate LCM of 268,820

Lowest Common Multiple of 268,820 using Common Division

2	268, 820
2	134, 410
	67, 205

∴ So the LCM of the given numbers is 2 x 2 x 67 x 205 = 54940

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/54940

Therefore, the GCF of Fractions 874/268,2710/820 is 2/54940

Least Common Multiple of 268,820 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 268,820 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(268,820) = 4

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

GCF(268,820) x common factors =4 x 1 = 4

LCM(268,820) = ( 268 × 820 ) / 4

LCM(268,820) = 219760 / 4

LCM(268,820) = 54940

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FAQs on GCF of Fractions of 874/268, 2710/820

1. What is the HCF of 874,2710?

The HCF of 874,2710 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 874/268, 2710/820?

Answer: GCF of Numerators as per given numbers 874/268, 2710/820 is

GCF of Numerators i.e. for 874,2710 is 2

LCM of denominators i.e. for 268,820 is 54940.

Thus, GCF of Fractions is 2/54940.Finally, GCF of Fractions for 874/268, 2710/820 is 2/54940.