How to Find GCF of 2809/229, 3478/1735?

GCF of 2809/229, 3478/1735

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 2809/229, 3478/1735 i.e 1/397315 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2809/229, 3478/1735.

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 2809/229,3478/1735?

Given fractions are 2809/229,3478/1735

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 2809/229,3478/1735, numerators are 2809,3478

Denominators are 229,1735

The GCF of 2809,3478 is 1 .

LCM of 229,1735 is 397315.

The greatest common factor of 2809/229,3478/1735 = [GCF of 2809,3478]/[LCM of 229,1735]= 1/397315

Therefore, the GCF of 2809/229,3478/1735 is 1/397315.

Greatest Common Factor of 2809,3478

To find the highest common factor of 2809,3478, we have to find the factors of both numbers and list the highest common factor.

The factors of 2809 are 1, 53, 2809

The factors of 3478 are 1, 2, 37, 47, 74, 94, 1739, 3478

The HCF of 2809,3478 is 1.

Lets's calculate GCF of 2809,3478

Greatest Common Factor (GCF) of 2809,3478 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 2809,3478 By Matching Biggest Common Factor Method

Now, list down the factors of 2809

1,53,2809

Now, list down the factors of 3478

1,2,37,47,74,94,1739,3478

Greatest Common Factor

We found the factors 2809,3478 . The biggest common factor number is the GCF number.
So the greatest common factor 2809,3478 is 1.

Lets's calculate LCM of 229,1735

Lowest Common Multiple of 229,1735 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 397315

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/397315

Therefore, the GCF of Fractions 2809/229,3478/1735 is 1/397315

Least Common Multiple of 229,1735 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 229,1735 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(229,1735) = 1

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

GCF(229,1735) x common factors =1 x 1 = 1

LCM(229,1735) = ( 229 × 1735 ) / 1

LCM(229,1735) = 397315 / 1

LCM(229,1735) = 397315

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FAQs on GCF of Fractions of 2809/229, 3478/1735

1. What is the HCF of 2809,3478?

The HCF of 2809,3478 is 1

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 2809/229, 3478/1735?

Answer: GCF of Numerators as per given numbers 2809/229, 3478/1735 is

GCF of Numerators i.e. for 2809,3478 is 1

LCM of denominators i.e. for 229,1735 is 397315.

Thus, GCF of Fractions is 1/397315.Finally, GCF of Fractions for 2809/229, 3478/1735 is 1/397315.