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GCF of 654/460, 2334/431

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 654/460, 2334/431 i.e 6/198260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 654/460, 2334/431.

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 654/460,2334/431?

Given fractions are 654/460,2334/431

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 654/460,2334/431, numerators are 654,2334

Denominators are 460,431

The GCF of 654,2334 is 6 .

LCM of 460,431 is 198260.

The greatest common factor of 654/460,2334/431 = [GCF of 654,2334]/[LCM of 460,431]= 6/198260

Therefore, the GCF of 654/460,2334/431 is 6/198260.

Greatest Common Factor of 654,2334

To find the highest common factor of 654,2334, we have to find the factors of both numbers and list the highest common factor.

The factors of 654 are 1, 2, 3, 6, 109, 218, 327, 654

The factors of 2334 are 1, 2, 3, 6, 389, 778, 1167, 2334

The HCF of 654,2334 is 6.

Lets's calculate GCF of 654,2334

Greatest Common Factor (GCF) of 654,2334 By Common Division

2 654, 2334
3 327, 1167
109, 389

∴ So the GCF of the given numbers is 2 x 3 = 6

Greatest Common Factor of 654,2334 By Matching Biggest Common Factor Method

Greatest Common Factor of 654,2334 By Matching Biggest Common Factor Method

Now, list down the factors of 654

:

1,2,3,6,109,218,327,654

Now, list down the factors of 2334

:

1,2,3,6,389,778,1167,2334

Greatest Common Factor

We found the factors 654,2334 . The biggest common factor number is the GCF number.
So the greatest common factor 654,2334 is 6.

Lets's calculate LCM of 460,431

Lowest Common Multiple of 460,431 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 198260

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/198260

Therefore, the GCF of Fractions 654/460,2334/431 is 6/198260

Least Common Multiple of 460,431 with GCF Formula

Least Common Multiple of 460,431 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 460,431 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(460,431) = 1

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

GCF(460,431) x common factors =1 x 1 = 1

LCM(460,431) = ( 460 × 431 ) / 1

LCM(460,431) = 198260 / 1

LCM(460,431) = 198260


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FAQs on GCF of Fractions of 654/460, 2334/431

1. What is the HCF of 654,2334?

The HCF of 654,2334 is 6

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 654/460, 2334/431?

Answer: GCF of Numerators as per given numbers 654/460, 2334/431 is

GCF of Numerators i.e. for 654,2334 is 6

LCM of denominators i.e. for 460,431 is 198260.

Thus, GCF of Fractions is 6/198260.Finally, GCF of Fractions for 654/460, 2334/431 is 6/198260.