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GCF of 584/78, 872/859

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 584/78, 872/859 i.e 8/67002 easily. The following is the detailed procedure to determine the greatest common factor of fractions 584/78, 872/859.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 584/78,872/859?

Given fractions are 584/78,872/859

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 584/78,872/859, numerators are 584,872

Denominators are 78,859

The GCF of 584,872 is 8 .

LCM of 78,859 is 67002.

The greatest common factor of 584/78,872/859 = [GCF of 584,872]/[LCM of 78,859]= 8/67002

Therefore, the GCF of 584/78,872/859 is 8/67002.

Greatest Common Factor of 584,872

To find the highest common factor of 584,872, we have to find the factors of both numbers and list the highest common factor.

The factors of 584 are 1, 2, 4, 8, 73, 146, 292, 584

The factors of 872 are 1, 2, 4, 8, 109, 218, 436, 872

The HCF of 584,872 is 8.

Lets's calculate GCF of 584,872

Greatest Common Factor (GCF) of 584,872 By Common Division

2 584, 872
2 292, 436
2 146, 218
73, 109

∴ So the GCF of the given numbers is 2 x 2 x 2 = 8

Greatest Common Factor of 584,872 By Matching Biggest Common Factor Method

Greatest Common Factor of 584,872 By Matching Biggest Common Factor Method

Now, list down the factors of 584

:

1,2,4,8,73,146,292,584

Now, list down the factors of 872

:

1,2,4,8,109,218,436,872

Greatest Common Factor

We found the factors 584,872 . The biggest common factor number is the GCF number.
So the greatest common factor 584,872 is 8.

Lets's calculate LCM of 78,859

Lowest Common Multiple of 78,859 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 67002

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/67002

Therefore, the GCF of Fractions 584/78,872/859 is 8/67002

Least Common Multiple of 78,859 with GCF Formula

Least Common Multiple of 78,859 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 78,859 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,859) = 1

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

GCF(78,859) x common factors =1 x 1 = 1

LCM(78,859) = ( 78 × 859 ) / 1

LCM(78,859) = 67002 / 1

LCM(78,859) = 67002


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FAQs on GCF of Fractions of 584/78, 872/859

1. What is the HCF of 584,872?

The HCF of 584,872 is 8

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 584/78, 872/859?

Answer: GCF of Numerators as per given numbers 584/78, 872/859 is

GCF of Numerators i.e. for 584,872 is 8

LCM of denominators i.e. for 78,859 is 67002.

Thus, GCF of Fractions is 8/67002.Finally, GCF of Fractions for 584/78, 872/859 is 8/67002.