How to Find GCF of 286/305, 1870/2506?

GCF of 286/305, 1870/2506

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 286/305, 1870/2506 i.e 22/764330 easily. The following is the detailed procedure to determine the greatest common factor of fractions 286/305, 1870/2506.

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 286/305,1870/2506?

Given fractions are 286/305,1870/2506

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 286/305,1870/2506, numerators are 286,1870

Denominators are 305,2506

The GCF of 286,1870 is 22 .

LCM of 305,2506 is 764330.

The greatest common factor of 286/305,1870/2506 = [GCF of 286,1870]/[LCM of 305,2506]= 22/764330

Therefore, the GCF of 286/305,1870/2506 is 22/764330.

Greatest Common Factor of 286,1870

To find the highest common factor of 286,1870, we have to find the factors of both numbers and list the highest common factor.

The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286

The factors of 1870 are 1, 2, 5, 10, 11, 17, 22, 34, 55, 85, 110, 170, 187, 374, 935, 1870

The HCF of 286,1870 is 22.

Lets's calculate GCF of 286,1870

Greatest Common Factor (GCF) of 286,1870 By Common Division

2	286, 1870
11	143, 935
	13, 85

∴ So the GCF of the given numbers is 2 x 11 = 22

Greatest Common Factor of 286,1870 By Matching Biggest Common Factor Method

Now, list down the factors of 286

1,2,11,13,22,26,143,286

Now, list down the factors of 1870

1,2,5,10,11,17,22,34,55,85,110,170,187,374,935,1870

Greatest Common Factor

We found the factors 286,1870 . The biggest common factor number is the GCF number.
So the greatest common factor 286,1870 is 22.

Lets's calculate LCM of 305,2506

Lowest Common Multiple of 305,2506 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 764330

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/764330

Therefore, the GCF of Fractions 286/305,1870/2506 is 22/764330

Least Common Multiple of 305,2506 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 305,2506 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(305,2506) = 1

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

GCF(305,2506) x common factors =1 x 1 = 1

LCM(305,2506) = ( 305 × 2506 ) / 1

LCM(305,2506) = 764330 / 1

LCM(305,2506) = 764330

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FAQs on GCF of Fractions of 286/305, 1870/2506

1. What is the HCF of 286,1870?

The HCF of 286,1870 is 22

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 286/305, 1870/2506?

Answer: GCF of Numerators as per given numbers 286/305, 1870/2506 is

GCF of Numerators i.e. for 286,1870 is 22

LCM of denominators i.e. for 305,2506 is 764330.

Thus, GCF of Fractions is 22/764330.Finally, GCF of Fractions for 286/305, 1870/2506 is 22/764330.