How to Find GCF of 3666/580, 2678/7157?

GCF of 3666/580, 2678/7157

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 3666/580, 2678/7157 i.e 26/4151060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3666/580, 2678/7157.

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 3666/580,2678/7157?

Given fractions are 3666/580,2678/7157

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 3666/580,2678/7157, numerators are 3666,2678

Denominators are 580,7157

The GCF of 3666,2678 is 26 .

LCM of 580,7157 is 4151060.

The greatest common factor of 3666/580,2678/7157 = [GCF of 3666,2678]/[LCM of 580,7157]= 26/4151060

Therefore, the GCF of 3666/580,2678/7157 is 26/4151060.

Greatest Common Factor of 3666,2678

To find the highest common factor of 3666,2678, we have to find the factors of both numbers and list the highest common factor.

The factors of 3666 are 1, 2, 3, 6, 13, 26, 39, 47, 78, 94, 141, 282, 611, 1222, 1833, 3666

The factors of 2678 are 1, 2, 13, 26, 103, 206, 1339, 2678

The HCF of 3666,2678 is 26.

Lets's calculate GCF of 3666,2678

Greatest Common Factor (GCF) of 3666,2678 By Common Division

2	3666, 2678
13	1833, 1339
	141, 103

∴ So the GCF of the given numbers is 2 x 13 = 26

Greatest Common Factor of 3666,2678 By Matching Biggest Common Factor Method

Now, list down the factors of 3666

1,2,3,6,13,26,39,47,78,94,141,282,611,1222,1833,3666

Now, list down the factors of 2678

1,2,13,26,103,206,1339,2678

Greatest Common Factor

We found the factors 3666,2678 . The biggest common factor number is the GCF number.
So the greatest common factor 3666,2678 is 26.

Lets's calculate LCM of 580,7157

Lowest Common Multiple of 580,7157 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 4151060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 26/4151060

Therefore, the GCF of Fractions 3666/580,2678/7157 is 26/4151060

Least Common Multiple of 580,7157 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 580,7157 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(580,7157) = 1

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

GCF(580,7157) x common factors =1 x 1 = 1

LCM(580,7157) = ( 580 × 7157 ) / 1

LCM(580,7157) = 4151060 / 1

LCM(580,7157) = 4151060

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FAQs on GCF of Fractions of 3666/580, 2678/7157

1. What is the HCF of 3666,2678?

The HCF of 3666,2678 is 26

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 3666/580, 2678/7157?

Answer: GCF of Numerators as per given numbers 3666/580, 2678/7157 is

GCF of Numerators i.e. for 3666,2678 is 26

LCM of denominators i.e. for 580,7157 is 4151060.

Thus, GCF of Fractions is 26/4151060.Finally, GCF of Fractions for 3666/580, 2678/7157 is 26/4151060.