How to Find GCF of 1801/208, 2369/1586?

GCF of 1801/208, 2369/1586

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 1801/208, 2369/1586 i.e 1/12688 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1801/208, 2369/1586.

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 1801/208,2369/1586?

Given fractions are 1801/208,2369/1586

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 1801/208,2369/1586, numerators are 1801,2369

Denominators are 208,1586

The GCF of 1801,2369 is 1 .

LCM of 208,1586 is 12688.

The greatest common factor of 1801/208,2369/1586 = [GCF of 1801,2369]/[LCM of 208,1586]= 1/12688

Therefore, the GCF of 1801/208,2369/1586 is 1/12688.

Greatest Common Factor of 1801,2369

To find the highest common factor of 1801,2369, we have to find the factors of both numbers and list the highest common factor.

The factors of 1801 are 1, 1801

The factors of 2369 are 1, 23, 103, 2369

The HCF of 1801,2369 is 1.

Lets's calculate GCF of 1801,2369

Greatest Common Factor (GCF) of 1801,2369 By Common Division

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

Greatest Common Factor of 1801,2369 By Matching Biggest Common Factor Method

Now, list down the factors of 1801

1,1801

Now, list down the factors of 2369

1,23,103,2369

Greatest Common Factor

We found the factors 1801,2369 . The biggest common factor number is the GCF number.
So the greatest common factor 1801,2369 is 1.

Lets's calculate LCM of 208,1586

Lowest Common Multiple of 208,1586 using Common Division

2	208, 1586
13	104, 793
	8, 61

∴ So the LCM of the given numbers is 2 x 13 x 8 x 61 = 12688

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12688

Therefore, the GCF of Fractions 1801/208,2369/1586 is 1/12688

Least Common Multiple of 208,1586 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 208,1586 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(208,1586) = 26

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

GCF(208,1586) x common factors =26 x 1 = 26

LCM(208,1586) = ( 208 × 1586 ) / 26

LCM(208,1586) = 329888 / 26

LCM(208,1586) = 12688

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FAQs on GCF of Fractions of 1801/208, 2369/1586

1. What is the HCF of 1801,2369?

The HCF of 1801,2369 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 1801/208, 2369/1586?

Answer: GCF of Numerators as per given numbers 1801/208, 2369/1586 is

GCF of Numerators i.e. for 1801,2369 is 1

LCM of denominators i.e. for 208,1586 is 12688.

Thus, GCF of Fractions is 1/12688.Finally, GCF of Fractions for 1801/208, 2369/1586 is 1/12688.