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GCF of 723/66, 257/428

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 723/66, 257/428 i.e 1/14124 easily. The following is the detailed procedure to determine the greatest common factor of fractions 723/66, 257/428.

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 723/66,257/428?

Given fractions are 723/66,257/428

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 723/66,257/428, numerators are 723,257

Denominators are 66,428

The GCF of 723,257 is 1 .

LCM of 66,428 is 14124.

The greatest common factor of 723/66,257/428 = [GCF of 723,257]/[LCM of 66,428]= 1/14124

Therefore, the GCF of 723/66,257/428 is 1/14124.

Greatest Common Factor of 723,257

To find the highest common factor of 723,257, we have to find the factors of both numbers and list the highest common factor.

The factors of 723 are 1, 3, 241, 723

The factors of 257 are 1, 257

The HCF of 723,257 is 1.

Lets's calculate GCF of 723,257

Greatest Common Factor (GCF) of 723,257 By Common Division

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

Greatest Common Factor of 723,257 By Matching Biggest Common Factor Method

Greatest Common Factor of 723,257 By Matching Biggest Common Factor Method

Now, list down the factors of 723

:

1,3,241,723

Now, list down the factors of 257

:

1,257

Greatest Common Factor

We found the factors 723,257 . The biggest common factor number is the GCF number.
So the greatest common factor 723,257 is 1.

Lets's calculate LCM of 66,428

Lowest Common Multiple of 66,428 using Common Division

2 66, 428
33, 214

∴ So the LCM of the given numbers is 2 x 33 x 214 = 14124

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14124

Therefore, the GCF of Fractions 723/66,257/428 is 1/14124

Least Common Multiple of 66,428 with GCF Formula

Least Common Multiple of 66,428 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 66,428 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(66,428) = 2

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

GCF(66,428) x common factors =2 x 1 = 2

LCM(66,428) = ( 66 × 428 ) / 2

LCM(66,428) = 28248 / 2

LCM(66,428) = 14124


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FAQs on GCF of Fractions of 723/66, 257/428

1. What is the HCF of 723,257?

The HCF of 723,257 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 723/66, 257/428?

Answer: GCF of Numerators as per given numbers 723/66, 257/428 is

GCF of Numerators i.e. for 723,257 is 1

LCM of denominators i.e. for 66,428 is 14124.

Thus, GCF of Fractions is 1/14124.Finally, GCF of Fractions for 723/66, 257/428 is 1/14124.