How to Find GCF of 568/238, 728/723?

GCF of 568/238, 728/723

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 568/238, 728/723 i.e 8/172074 easily. The following is the detailed procedure to determine the greatest common factor of fractions 568/238, 728/723.

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 568/238,728/723?

Given fractions are 568/238,728/723

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 568/238,728/723, numerators are 568,728

Denominators are 238,723

The GCF of 568,728 is 8 .

LCM of 238,723 is 172074.

The greatest common factor of 568/238,728/723 = [GCF of 568,728]/[LCM of 238,723]= 8/172074

Therefore, the GCF of 568/238,728/723 is 8/172074.

Greatest Common Factor of 568,728

To find the highest common factor of 568,728, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

The HCF of 568,728 is 8.

Lets's calculate GCF of 568,728

Greatest Common Factor (GCF) of 568,728 By Common Division

2	568, 728
2	284, 364
2	142, 182
	71, 91

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

Greatest Common Factor of 568,728 By Matching Biggest Common Factor Method

Now, list down the factors of 568

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

Now, list down the factors of 728

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Greatest Common Factor

We found the factors 568,728 . The biggest common factor number is the GCF number.
So the greatest common factor 568,728 is 8.

Lets's calculate LCM of 238,723

Lowest Common Multiple of 238,723 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 172074

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/172074

Therefore, the GCF of Fractions 568/238,728/723 is 8/172074

Least Common Multiple of 238,723 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 238,723 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(238,723) = 1

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

GCF(238,723) x common factors =1 x 1 = 1

LCM(238,723) = ( 238 × 723 ) / 1

LCM(238,723) = 172074 / 1

LCM(238,723) = 172074

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FAQs on GCF of Fractions of 568/238, 728/723

1. What is the HCF of 568,728?

The HCF of 568,728 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 568/238, 728/723?

Answer: GCF of Numerators as per given numbers 568/238, 728/723 is

GCF of Numerators i.e. for 568,728 is 8

LCM of denominators i.e. for 238,723 is 172074.

Thus, GCF of Fractions is 8/172074.Finally, GCF of Fractions for 568/238, 728/723 is 8/172074.