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GCF of 419/198, 406/111

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 419/198, 406/111 i.e 1/7326 easily. The following is the detailed procedure to determine the greatest common factor of fractions 419/198, 406/111.

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 419/198,406/111?

Given fractions are 419/198,406/111

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 419/198,406/111, numerators are 419,406

Denominators are 198,111

The GCF of 419,406 is 1 .

LCM of 198,111 is 7326.

The greatest common factor of 419/198,406/111 = [GCF of 419,406]/[LCM of 198,111]= 1/7326

Therefore, the GCF of 419/198,406/111 is 1/7326.

Greatest Common Factor of 419,406

To find the highest common factor of 419,406, we have to find the factors of both numbers and list the highest common factor.

The factors of 419 are 1, 419

The factors of 406 are 1, 2, 7, 14, 29, 58, 203, 406

The HCF of 419,406 is 1.

Lets's calculate GCF of 419,406

Greatest Common Factor (GCF) of 419,406 By Common Division

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

Greatest Common Factor of 419,406 By Matching Biggest Common Factor Method

Greatest Common Factor of 419,406 By Matching Biggest Common Factor Method

Now, list down the factors of 419

:

1,419

Now, list down the factors of 406

:

1,2,7,14,29,58,203,406

Greatest Common Factor

We found the factors 419,406 . The biggest common factor number is the GCF number.
So the greatest common factor 419,406 is 1.

Lets's calculate LCM of 198,111

Lowest Common Multiple of 198,111 using Common Division

3 198, 111
66, 37

∴ So the LCM of the given numbers is 3 x 66 x 37 = 7326

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7326

Therefore, the GCF of Fractions 419/198,406/111 is 1/7326

Least Common Multiple of 198,111 with GCF Formula

Least Common Multiple of 198,111 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 198,111 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(198,111) = 3

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

GCF(198,111) x common factors =3 x 1 = 3

LCM(198,111) = ( 198 × 111 ) / 3

LCM(198,111) = 21978 / 3

LCM(198,111) = 7326


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FAQs on GCF of Fractions of 419/198, 406/111

1. What is the HCF of 419,406?

The HCF of 419,406 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 419/198, 406/111?

Answer: GCF of Numerators as per given numbers 419/198, 406/111 is

GCF of Numerators i.e. for 419,406 is 1

LCM of denominators i.e. for 198,111 is 7326.

Thus, GCF of Fractions is 1/7326.Finally, GCF of Fractions for 419/198, 406/111 is 1/7326.