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GCF of 392/54, 449/658

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 392/54, 449/658 i.e 1/17766 easily. The following is the detailed procedure to determine the greatest common factor of fractions 392/54, 449/658.

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 392/54,449/658?

Given fractions are 392/54,449/658

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 392/54,449/658, numerators are 392,449

Denominators are 54,658

The GCF of 392,449 is 1 .

LCM of 54,658 is 17766.

The greatest common factor of 392/54,449/658 = [GCF of 392,449]/[LCM of 54,658]= 1/17766

Therefore, the GCF of 392/54,449/658 is 1/17766.

Greatest Common Factor of 392,449

To find the highest common factor of 392,449, we have to find the factors of both numbers and list the highest common factor.

The factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392

The factors of 449 are 1, 449

The HCF of 392,449 is 1.

Lets's calculate GCF of 392,449

Greatest Common Factor (GCF) of 392,449 By Common Division

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

Greatest Common Factor of 392,449 By Matching Biggest Common Factor Method

Greatest Common Factor of 392,449 By Matching Biggest Common Factor Method

Now, list down the factors of 392

:

1,2,4,7,8,14,28,49,56,98,196,392

Now, list down the factors of 449

:

1,449

Greatest Common Factor

We found the factors 392,449 . The biggest common factor number is the GCF number.
So the greatest common factor 392,449 is 1.

Lets's calculate LCM of 54,658

Lowest Common Multiple of 54,658 using Common Division

2 54, 658
27, 329

∴ So the LCM of the given numbers is 2 x 27 x 329 = 17766

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17766

Therefore, the GCF of Fractions 392/54,449/658 is 1/17766

Least Common Multiple of 54,658 with GCF Formula

Least Common Multiple of 54,658 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 54,658 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(54,658) = 2

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

GCF(54,658) x common factors =2 x 1 = 2

LCM(54,658) = ( 54 × 658 ) / 2

LCM(54,658) = 35532 / 2

LCM(54,658) = 17766


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FAQs on GCF of Fractions of 392/54, 449/658

1. What is the HCF of 392,449?

The HCF of 392,449 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 392/54, 449/658?

Answer: GCF of Numerators as per given numbers 392/54, 449/658 is

GCF of Numerators i.e. for 392,449 is 1

LCM of denominators i.e. for 54,658 is 17766.

Thus, GCF of Fractions is 1/17766.Finally, GCF of Fractions for 392/54, 449/658 is 1/17766.