How to Find GCF of 289/1719, 867/3230?

GCF of 289/1719, 867/3230

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 289/1719, 867/3230 i.e 289/5552370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 289/1719, 867/3230.

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 289/1719,867/3230?

Given fractions are 289/1719,867/3230

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 289/1719,867/3230, numerators are 289,867

Denominators are 1719,3230

The GCF of 289,867 is 289 .

LCM of 1719,3230 is 5552370.

The greatest common factor of 289/1719,867/3230 = [GCF of 289,867]/[LCM of 1719,3230]= 289/5552370

Therefore, the GCF of 289/1719,867/3230 is 289/5552370.

Greatest Common Factor of 289,867

To find the highest common factor of 289,867, we have to find the factors of both numbers and list the highest common factor.

The factors of 289 are 1, 17, 289

The factors of 867 are 1, 3, 17, 51, 289, 867

The HCF of 289,867 is 289.

Lets's calculate GCF of 289,867

Greatest Common Factor (GCF) of 289,867 By Common Division

17	289, 867
17	17, 51
	1, 3

∴ So the GCF of the given numbers is 17 x 17 = 289

Greatest Common Factor of 289,867 By Matching Biggest Common Factor Method

Now, list down the factors of 289

1,17,289

Now, list down the factors of 867

1,3,17,51,289,867

Greatest Common Factor

We found the factors 289,867 . The biggest common factor number is the GCF number.
So the greatest common factor 289,867 is 289.

Lets's calculate LCM of 1719,3230

Lowest Common Multiple of 1719,3230 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 5552370

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 289/5552370

Therefore, the GCF of Fractions 289/1719,867/3230 is 289/5552370

Least Common Multiple of 1719,3230 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 1719,3230 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(1719,3230) = 1

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

GCF(1719,3230) x common factors =1 x 1 = 1

LCM(1719,3230) = ( 1719 × 3230 ) / 1

LCM(1719,3230) = 5552370 / 1

LCM(1719,3230) = 5552370

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FAQs on GCF of Fractions of 289/1719, 867/3230

1. What is the HCF of 289,867?

The HCF of 289,867 is 289

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 289/1719, 867/3230?

Answer: GCF of Numerators as per given numbers 289/1719, 867/3230 is

GCF of Numerators i.e. for 289,867 is 289

LCM of denominators i.e. for 1719,3230 is 5552370.

Thus, GCF of Fractions is 289/5552370.Finally, GCF of Fractions for 289/1719, 867/3230 is 289/5552370.