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GCF of 658/978, 321/500

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 658/978, 321/500 i.e 1/244500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 658/978, 321/500.

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 658/978,321/500?

Given fractions are 658/978,321/500

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 658/978,321/500, numerators are 658,321

Denominators are 978,500

The GCF of 658,321 is 1 .

LCM of 978,500 is 244500.

The greatest common factor of 658/978,321/500 = [GCF of 658,321]/[LCM of 978,500]= 1/244500

Therefore, the GCF of 658/978,321/500 is 1/244500.

Greatest Common Factor of 658,321

To find the highest common factor of 658,321, we have to find the factors of both numbers and list the highest common factor.

The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658

The factors of 321 are 1, 3, 107, 321

The HCF of 658,321 is 1.

Lets's calculate GCF of 658,321

Greatest Common Factor (GCF) of 658,321 By Common Division

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

Greatest Common Factor of 658,321 By Matching Biggest Common Factor Method

Greatest Common Factor of 658,321 By Matching Biggest Common Factor Method

Now, list down the factors of 658

:

1,2,7,14,47,94,329,658

Now, list down the factors of 321

:

1,3,107,321

Greatest Common Factor

We found the factors 658,321 . The biggest common factor number is the GCF number.
So the greatest common factor 658,321 is 1.

Lets's calculate LCM of 978,500

Lowest Common Multiple of 978,500 using Common Division

2 978, 500
489, 250

∴ So the LCM of the given numbers is 2 x 489 x 250 = 244500

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/244500

Therefore, the GCF of Fractions 658/978,321/500 is 1/244500

Least Common Multiple of 978,500 with GCF Formula

Least Common Multiple of 978,500 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 978,500 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(978,500) = 2

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

GCF(978,500) x common factors =2 x 1 = 2

LCM(978,500) = ( 978 × 500 ) / 2

LCM(978,500) = 489000 / 2

LCM(978,500) = 244500


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FAQs on GCF of Fractions of 658/978, 321/500

1. What is the HCF of 658,321?

The HCF of 658,321 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 658/978, 321/500?

Answer: GCF of Numerators as per given numbers 658/978, 321/500 is

GCF of Numerators i.e. for 658,321 is 1

LCM of denominators i.e. for 978,500 is 244500.

Thus, GCF of Fractions is 1/244500.Finally, GCF of Fractions for 658/978, 321/500 is 1/244500.