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GCF of 489/334, 431/164

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 489/334, 431/164 i.e 1/27388 easily. The following is the detailed procedure to determine the greatest common factor of fractions 489/334, 431/164.

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 489/334,431/164?

Given fractions are 489/334,431/164

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 489/334,431/164, numerators are 489,431

Denominators are 334,164

The GCF of 489,431 is 1 .

LCM of 334,164 is 27388.

The greatest common factor of 489/334,431/164 = [GCF of 489,431]/[LCM of 334,164]= 1/27388

Therefore, the GCF of 489/334,431/164 is 1/27388.

Greatest Common Factor of 489,431

To find the highest common factor of 489,431, we have to find the factors of both numbers and list the highest common factor.

The factors of 489 are 1, 3, 163, 489

The factors of 431 are 1, 431

The HCF of 489,431 is 1.

Lets's calculate GCF of 489,431

Greatest Common Factor (GCF) of 489,431 By Common Division

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

Greatest Common Factor of 489,431 By Matching Biggest Common Factor Method

Greatest Common Factor of 489,431 By Matching Biggest Common Factor Method

Now, list down the factors of 489

:

1,3,163,489

Now, list down the factors of 431

:

1,431

Greatest Common Factor

We found the factors 489,431 . The biggest common factor number is the GCF number.
So the greatest common factor 489,431 is 1.

Lets's calculate LCM of 334,164

Lowest Common Multiple of 334,164 using Common Division

2 334, 164
167, 82

∴ So the LCM of the given numbers is 2 x 167 x 82 = 27388

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/27388

Therefore, the GCF of Fractions 489/334,431/164 is 1/27388

Least Common Multiple of 334,164 with GCF Formula

Least Common Multiple of 334,164 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 334,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(334,164) = 2

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

GCF(334,164) x common factors =2 x 1 = 2

LCM(334,164) = ( 334 × 164 ) / 2

LCM(334,164) = 54776 / 2

LCM(334,164) = 27388


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FAQs on GCF of Fractions of 489/334, 431/164

1. What is the HCF of 489,431?

The HCF of 489,431 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 489/334, 431/164?

Answer: GCF of Numerators as per given numbers 489/334, 431/164 is

GCF of Numerators i.e. for 489,431 is 1

LCM of denominators i.e. for 334,164 is 27388.

Thus, GCF of Fractions is 1/27388.Finally, GCF of Fractions for 489/334, 431/164 is 1/27388.