How to Find GCF of 298/353, 1991/1823?

GCF of 298/353, 1991/1823

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 298/353, 1991/1823 i.e 1/643519 easily. The following is the detailed procedure to determine the greatest common factor of fractions 298/353, 1991/1823.

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 298/353,1991/1823?

Given fractions are 298/353,1991/1823

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 298/353,1991/1823, numerators are 298,1991

Denominators are 353,1823

The GCF of 298,1991 is 1 .

LCM of 353,1823 is 643519.

The greatest common factor of 298/353,1991/1823 = [GCF of 298,1991]/[LCM of 353,1823]= 1/643519

Therefore, the GCF of 298/353,1991/1823 is 1/643519.

Greatest Common Factor of 298,1991

To find the highest common factor of 298,1991, we have to find the factors of both numbers and list the highest common factor.

The factors of 298 are 1, 2, 149, 298

The factors of 1991 are 1, 11, 181, 1991

The HCF of 298,1991 is 1.

Lets's calculate GCF of 298,1991

Greatest Common Factor (GCF) of 298,1991 By Common Division

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

Greatest Common Factor of 298,1991 By Matching Biggest Common Factor Method

Now, list down the factors of 298

1,2,149,298

Now, list down the factors of 1991

1,11,181,1991

Greatest Common Factor

We found the factors 298,1991 . The biggest common factor number is the GCF number.
So the greatest common factor 298,1991 is 1.

Lets's calculate LCM of 353,1823

Lowest Common Multiple of 353,1823 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 643519

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/643519

Therefore, the GCF of Fractions 298/353,1991/1823 is 1/643519

Least Common Multiple of 353,1823 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 353,1823 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(353,1823) = 1

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

GCF(353,1823) x common factors =1 x 1 = 1

LCM(353,1823) = ( 353 × 1823 ) / 1

LCM(353,1823) = 643519 / 1

LCM(353,1823) = 643519

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FAQs on GCF of Fractions of 298/353, 1991/1823

1. What is the HCF of 298,1991?

The HCF of 298,1991 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 298/353, 1991/1823?

Answer: GCF of Numerators as per given numbers 298/353, 1991/1823 is

GCF of Numerators i.e. for 298,1991 is 1

LCM of denominators i.e. for 353,1823 is 643519.

Thus, GCF of Fractions is 1/643519.Finally, GCF of Fractions for 298/353, 1991/1823 is 1/643519.