How to Find GCF of 80/23, 82/84, 568/205?

GCF of 80/23, 82/84, 568/205

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 80/23, 82/84, 568/205 i.e 2/396060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 80/23, 82/84, 568/205.

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 80/23,82/84,568/205?

Given fractions are 80/23,82/84,568/205

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 80/23,82/84,568/205, numerators are 80,82,568

Denominators are 23,84,205

The GCF of 80,82,568 is 2 .

LCM of 23,84,205 is 396060.

The greatest common factor of 80/23,82/84,568/205 = [GCF of 80,82,568]/[LCM of 23,84,205]= 2/396060

Therefore, the GCF of 80/23,82/84,568/205 is 2/396060.

Greatest Common Factor of 80,82,568

To find the highest common factor of 80,82,568, we have to find the factors of both numbers and list the highest common factor.

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

The factors of 82 are 1, 2, 41, 82

The factors of 568 are 1, 2, 4, 8, 71, 142, 284, 568

The HCF of 80,82,568 is 2.

Lets's calculate GCF of 80,82,568

Greatest Common Factor (GCF) of 80,82,568 By Common Division

2	80, 82, 568
	40, 41, 284

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

Greatest Common Factor of 80,82,568 By Matching Biggest Common Factor Method

Now, list down the factors of 80

1,2,4,5,8,10,16,20,40,80

Now, list down the factors of 82

1,2,41,82

Now, list down the factors of 568

1,2,4,8,71,142,284,568

Greatest Common Factor

We found the factors 80,82,568 . The biggest common factor number is the GCF number.
So the greatest common factor 80,82,568 is 2.

Lets's calculate LCM of 23,84,205

Lowest Common Multiple of 23,84,205 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 396060

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/396060

Therefore, the GCF of Fractions 80/23,82/84,568/205 is 2/396060

Least Common Multiple of 23,84,205 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 23,84,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,84,205) = 1

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

GCF(23,84,205) x common factors =1 x 1 = 1

LCM(23,84,205) = ( 23 × 84 × 205 ) / 1

LCM(23,84,205) = 396060 / 1

LCM(23,84,205) = 396060

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FAQs on GCF of Fractions of 80/23, 82/84, 568/205

1. What is the HCF of 80,82,568?

The HCF of 80,82,568 is 2

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 80/23, 82/84, 568/205?

Answer: GCF of Numerators as per given numbers 80/23, 82/84, 568/205 is

GCF of Numerators i.e. for 80,82,568 is 2

LCM of denominators i.e. for 23,84,205 is 396060.

Thus, GCF of Fractions is 2/396060.Finally, GCF of Fractions for 80/23, 82/84, 568/205 is 2/396060.