How to Find GCF of 6578/866, 5889/7674?

GCF of 6578/866, 5889/7674

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 6578/866, 5889/7674 i.e 13/3322842 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6578/866, 5889/7674.

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 6578/866,5889/7674?

Given fractions are 6578/866,5889/7674

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 6578/866,5889/7674, numerators are 6578,5889

Denominators are 866,7674

The GCF of 6578,5889 is 13 .

LCM of 866,7674 is 3322842.

The greatest common factor of 6578/866,5889/7674 = [GCF of 6578,5889]/[LCM of 866,7674]= 13/3322842

Therefore, the GCF of 6578/866,5889/7674 is 13/3322842.

Greatest Common Factor of 6578,5889

To find the highest common factor of 6578,5889, we have to find the factors of both numbers and list the highest common factor.

The factors of 6578 are 1, 2, 11, 13, 22, 23, 26, 46, 143, 253, 286, 299, 506, 598, 3289, 6578

The factors of 5889 are 1, 3, 13, 39, 151, 453, 1963, 5889

The HCF of 6578,5889 is 13.

Lets's calculate GCF of 6578,5889

Greatest Common Factor (GCF) of 6578,5889 By Common Division

13	6578, 5889
	506, 453

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 6578,5889 By Matching Biggest Common Factor Method

Now, list down the factors of 6578

1,2,11,13,22,23,26,46,143,253,286,299,506,598,3289,6578

Now, list down the factors of 5889

1,3,13,39,151,453,1963,5889

Greatest Common Factor

We found the factors 6578,5889 . The biggest common factor number is the GCF number.
So the greatest common factor 6578,5889 is 13.

Lets's calculate LCM of 866,7674

Lowest Common Multiple of 866,7674 using Common Division

2	866, 7674
	433, 3837

∴ So the LCM of the given numbers is 2 x 433 x 3837 = 3322842

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/3322842

Therefore, the GCF of Fractions 6578/866,5889/7674 is 13/3322842

Least Common Multiple of 866,7674 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 866,7674 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(866,7674) = 2

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

GCF(866,7674) x common factors =2 x 1 = 2

LCM(866,7674) = ( 866 × 7674 ) / 2

LCM(866,7674) = 6645684 / 2

LCM(866,7674) = 3322842

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 6578/866, 5889/7674

1. What is the HCF of 6578,5889?

The HCF of 6578,5889 is 13

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 6578/866, 5889/7674?

Answer: GCF of Numerators as per given numbers 6578/866, 5889/7674 is

GCF of Numerators i.e. for 6578,5889 is 13

LCM of denominators i.e. for 866,7674 is 3322842.

Thus, GCF of Fractions is 13/3322842.Finally, GCF of Fractions for 6578/866, 5889/7674 is 13/3322842.