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GCF of 230/289, 365/277

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 230/289, 365/277 i.e 5/80053 easily. The following is the detailed procedure to determine the greatest common factor of fractions 230/289, 365/277.

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 230/289,365/277?

Given fractions are 230/289,365/277

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 230/289,365/277, numerators are 230,365

Denominators are 289,277

The GCF of 230,365 is 5 .

LCM of 289,277 is 80053.

The greatest common factor of 230/289,365/277 = [GCF of 230,365]/[LCM of 289,277]= 5/80053

Therefore, the GCF of 230/289,365/277 is 5/80053.

Greatest Common Factor of 230,365

To find the highest common factor of 230,365, we have to find the factors of both numbers and list the highest common factor.

The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230

The factors of 365 are 1, 5, 73, 365

The HCF of 230,365 is 5.

Lets's calculate GCF of 230,365

Greatest Common Factor (GCF) of 230,365 By Common Division

5 230, 365
46, 73

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 230,365 By Matching Biggest Common Factor Method

Greatest Common Factor of 230,365 By Matching Biggest Common Factor Method

Now, list down the factors of 230

:

1,2,5,10,23,46,115,230

Now, list down the factors of 365

:

1,5,73,365

Greatest Common Factor

We found the factors 230,365 . The biggest common factor number is the GCF number.
So the greatest common factor 230,365 is 5.

Lets's calculate LCM of 289,277

Lowest Common Multiple of 289,277 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 80053

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/80053

Therefore, the GCF of Fractions 230/289,365/277 is 5/80053

Least Common Multiple of 289,277 with GCF Formula

Least Common Multiple of 289,277 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 289,277 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(289,277) = 1

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

GCF(289,277) x common factors =1 x 1 = 1

LCM(289,277) = ( 289 × 277 ) / 1

LCM(289,277) = 80053 / 1

LCM(289,277) = 80053


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 230/289, 365/277

1. What is the HCF of 230,365?

The HCF of 230,365 is 5

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 230/289, 365/277?

Answer: GCF of Numerators as per given numbers 230/289, 365/277 is

GCF of Numerators i.e. for 230,365 is 5

LCM of denominators i.e. for 289,277 is 80053.

Thus, GCF of Fractions is 5/80053.Finally, GCF of Fractions for 230/289, 365/277 is 5/80053.