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GCF of 419/402, 500/268

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 419/402, 500/268 i.e 1/804 easily. The following is the detailed procedure to determine the greatest common factor of fractions 419/402, 500/268.

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 419/402,500/268?

Given fractions are 419/402,500/268

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 419/402,500/268, numerators are 419,500

Denominators are 402,268

The GCF of 419,500 is 1 .

LCM of 402,268 is 804.

The greatest common factor of 419/402,500/268 = [GCF of 419,500]/[LCM of 402,268]= 1/804

Therefore, the GCF of 419/402,500/268 is 1/804.

Greatest Common Factor of 419,500

To find the highest common factor of 419,500, 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 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

The HCF of 419,500 is 1.

Lets's calculate GCF of 419,500

Greatest Common Factor (GCF) of 419,500 By Common Division

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

Greatest Common Factor of 419,500 By Matching Biggest Common Factor Method

Greatest Common Factor of 419,500 By Matching Biggest Common Factor Method

Now, list down the factors of 419

:

1,419

Now, list down the factors of 500

:

1,2,4,5,10,20,25,50,100,125,250,500

Greatest Common Factor

We found the factors 419,500 . The biggest common factor number is the GCF number.
So the greatest common factor 419,500 is 1.

Lets's calculate LCM of 402,268

Lowest Common Multiple of 402,268 using Common Division

2 402, 268
67 201, 134
3, 2

∴ So the LCM of the given numbers is 2 x 67 x 3 x 2 = 804

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/804

Therefore, the GCF of Fractions 419/402,500/268 is 1/804

Least Common Multiple of 402,268 with GCF Formula

Least Common Multiple of 402,268 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 402,268 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(402,268) = 134

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

GCF(402,268) x common factors =134 x 1 = 134

LCM(402,268) = ( 402 × 268 ) / 134

LCM(402,268) = 107736 / 134

LCM(402,268) = 804


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FAQs on GCF of Fractions of 419/402, 500/268

1. What is the HCF of 419,500?

The HCF of 419,500 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 419/402, 500/268?

Answer: GCF of Numerators as per given numbers 419/402, 500/268 is

GCF of Numerators i.e. for 419,500 is 1

LCM of denominators i.e. for 402,268 is 804.

Thus, GCF of Fractions is 1/804.Finally, GCF of Fractions for 419/402, 500/268 is 1/804.