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GCF of 428/270, 323/522

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 428/270, 323/522 i.e 1/7830 easily. The following is the detailed procedure to determine the greatest common factor of fractions 428/270, 323/522.

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 428/270,323/522?

Given fractions are 428/270,323/522

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 428/270,323/522, numerators are 428,323

Denominators are 270,522

The GCF of 428,323 is 1 .

LCM of 270,522 is 7830.

The greatest common factor of 428/270,323/522 = [GCF of 428,323]/[LCM of 270,522]= 1/7830

Therefore, the GCF of 428/270,323/522 is 1/7830.

Greatest Common Factor of 428,323

To find the highest common factor of 428,323, we have to find the factors of both numbers and list the highest common factor.

The factors of 428 are 1, 2, 4, 107, 214, 428

The factors of 323 are 1, 17, 19, 323

The HCF of 428,323 is 1.

Lets's calculate GCF of 428,323

Greatest Common Factor (GCF) of 428,323 By Common Division

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

Greatest Common Factor of 428,323 By Matching Biggest Common Factor Method

Greatest Common Factor of 428,323 By Matching Biggest Common Factor Method

Now, list down the factors of 428

:

1,2,4,107,214,428

Now, list down the factors of 323

:

1,17,19,323

Greatest Common Factor

We found the factors 428,323 . The biggest common factor number is the GCF number.
So the greatest common factor 428,323 is 1.

Lets's calculate LCM of 270,522

Lowest Common Multiple of 270,522 using Common Division

2 270, 522
3 135, 261
3 45, 87
15, 29

∴ So the LCM of the given numbers is 2 x 3 x 3 x 15 x 29 = 7830

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7830

Therefore, the GCF of Fractions 428/270,323/522 is 1/7830

Least Common Multiple of 270,522 with GCF Formula

Least Common Multiple of 270,522 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 270,522 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(270,522) = 18

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

GCF(270,522) x common factors =18 x 1 = 18

LCM(270,522) = ( 270 × 522 ) / 18

LCM(270,522) = 140940 / 18

LCM(270,522) = 7830


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FAQs on GCF of Fractions of 428/270, 323/522

1. What is the HCF of 428,323?

The HCF of 428,323 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 428/270, 323/522?

Answer: GCF of Numerators as per given numbers 428/270, 323/522 is

GCF of Numerators i.e. for 428,323 is 1

LCM of denominators i.e. for 270,522 is 7830.

Thus, GCF of Fractions is 1/7830.Finally, GCF of Fractions for 428/270, 323/522 is 1/7830.