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GCF of 398/30, 523/259

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 398/30, 523/259 i.e 1/7770 easily. The following is the detailed procedure to determine the greatest common factor of fractions 398/30, 523/259.

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 398/30,523/259?

Given fractions are 398/30,523/259

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 398/30,523/259, numerators are 398,523

Denominators are 30,259

The GCF of 398,523 is 1 .

LCM of 30,259 is 7770.

The greatest common factor of 398/30,523/259 = [GCF of 398,523]/[LCM of 30,259]= 1/7770

Therefore, the GCF of 398/30,523/259 is 1/7770.

Greatest Common Factor of 398,523

To find the highest common factor of 398,523, we have to find the factors of both numbers and list the highest common factor.

The factors of 398 are 1, 2, 199, 398

The factors of 523 are 1, 523

The HCF of 398,523 is 1.

Lets's calculate GCF of 398,523

Greatest Common Factor (GCF) of 398,523 By Common Division

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

Greatest Common Factor of 398,523 By Matching Biggest Common Factor Method

Greatest Common Factor of 398,523 By Matching Biggest Common Factor Method

Now, list down the factors of 398

:

1,2,199,398

Now, list down the factors of 523

:

1,523

Greatest Common Factor

We found the factors 398,523 . The biggest common factor number is the GCF number.
So the greatest common factor 398,523 is 1.

Lets's calculate LCM of 30,259

Lowest Common Multiple of 30,259 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 7770

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7770

Therefore, the GCF of Fractions 398/30,523/259 is 1/7770

Least Common Multiple of 30,259 with GCF Formula

Least Common Multiple of 30,259 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 30,259 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(30,259) = 1

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

GCF(30,259) x common factors =1 x 1 = 1

LCM(30,259) = ( 30 × 259 ) / 1

LCM(30,259) = 7770 / 1

LCM(30,259) = 7770


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FAQs on GCF of Fractions of 398/30, 523/259

1. What is the HCF of 398,523?

The HCF of 398,523 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 398/30, 523/259?

Answer: GCF of Numerators as per given numbers 398/30, 523/259 is

GCF of Numerators i.e. for 398,523 is 1

LCM of denominators i.e. for 30,259 is 7770.

Thus, GCF of Fractions is 1/7770.Finally, GCF of Fractions for 398/30, 523/259 is 1/7770.