How to Find GCF of 188/807, 564/259?

GCF of 188/807, 564/259

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 188/807, 564/259 i.e 188/209013 easily. The following is the detailed procedure to determine the greatest common factor of fractions 188/807, 564/259.

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 188/807,564/259?

Given fractions are 188/807,564/259

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 188/807,564/259, numerators are 188,564

Denominators are 807,259

The GCF of 188,564 is 188 .

LCM of 807,259 is 209013.

The greatest common factor of 188/807,564/259 = [GCF of 188,564]/[LCM of 807,259]= 188/209013

Therefore, the GCF of 188/807,564/259 is 188/209013.

Greatest Common Factor of 188,564

To find the highest common factor of 188,564, we have to find the factors of both numbers and list the highest common factor.

The factors of 188 are 1, 2, 4, 47, 94, 188

The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564

The HCF of 188,564 is 188.

Lets's calculate GCF of 188,564

Greatest Common Factor (GCF) of 188,564 By Common Division

2	188, 564
2	94, 282
47	47, 141
	1, 3

∴ So the GCF of the given numbers is 2 x 2 x 47 = 188

Greatest Common Factor of 188,564 By Matching Biggest Common Factor Method

Now, list down the factors of 188

1,2,4,47,94,188

Now, list down the factors of 564

1,2,3,4,6,12,47,94,141,188,282,564

Greatest Common Factor

We found the factors 188,564 . The biggest common factor number is the GCF number.
So the greatest common factor 188,564 is 188.

Lets's calculate LCM of 807,259

Lowest Common Multiple of 807,259 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 209013

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 188/209013

Therefore, the GCF of Fractions 188/807,564/259 is 188/209013

Least Common Multiple of 807,259 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 807,259 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(807,259) = 1

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

GCF(807,259) x common factors =1 x 1 = 1

LCM(807,259) = ( 807 × 259 ) / 1

LCM(807,259) = 209013 / 1

LCM(807,259) = 209013

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FAQs on GCF of Fractions of 188/807, 564/259

1. What is the HCF of 188,564?

The HCF of 188,564 is 188

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 188/807, 564/259?

Answer: GCF of Numerators as per given numbers 188/807, 564/259 is

GCF of Numerators i.e. for 188,564 is 188

LCM of denominators i.e. for 807,259 is 209013.

Thus, GCF of Fractions is 188/209013.Finally, GCF of Fractions for 188/807, 564/259 is 188/209013.