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GCF of 285/511, 678/590

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 285/511, 678/590 i.e 3/301490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 285/511, 678/590.

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 285/511,678/590?

Given fractions are 285/511,678/590

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 285/511,678/590, numerators are 285,678

Denominators are 511,590

The GCF of 285,678 is 3 .

LCM of 511,590 is 301490.

The greatest common factor of 285/511,678/590 = [GCF of 285,678]/[LCM of 511,590]= 3/301490

Therefore, the GCF of 285/511,678/590 is 3/301490.

Greatest Common Factor of 285,678

To find the highest common factor of 285,678, we have to find the factors of both numbers and list the highest common factor.

The factors of 285 are 1, 3, 5, 15, 19, 57, 95, 285

The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678

The HCF of 285,678 is 3.

Lets's calculate GCF of 285,678

Greatest Common Factor (GCF) of 285,678 By Common Division

3 285, 678
95, 226

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 285,678 By Matching Biggest Common Factor Method

Greatest Common Factor of 285,678 By Matching Biggest Common Factor Method

Now, list down the factors of 285

:

1,3,5,15,19,57,95,285

Now, list down the factors of 678

:

1,2,3,6,113,226,339,678

Greatest Common Factor

We found the factors 285,678 . The biggest common factor number is the GCF number.
So the greatest common factor 285,678 is 3.

Lets's calculate LCM of 511,590

Lowest Common Multiple of 511,590 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 301490

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/301490

Therefore, the GCF of Fractions 285/511,678/590 is 3/301490

Least Common Multiple of 511,590 with GCF Formula

Least Common Multiple of 511,590 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 511,590 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(511,590) = 1

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

GCF(511,590) x common factors =1 x 1 = 1

LCM(511,590) = ( 511 × 590 ) / 1

LCM(511,590) = 301490 / 1

LCM(511,590) = 301490


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FAQs on GCF of Fractions of 285/511, 678/590

1. What is the HCF of 285,678?

The HCF of 285,678 is 3

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 285/511, 678/590?

Answer: GCF of Numerators as per given numbers 285/511, 678/590 is

GCF of Numerators i.e. for 285,678 is 3

LCM of denominators i.e. for 511,590 is 301490.

Thus, GCF of Fractions is 3/301490.Finally, GCF of Fractions for 285/511, 678/590 is 3/301490.