How to Find GCF of 730/404, 978/501?

GCF of 730/404, 978/501

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 730/404, 978/501 i.e 2/202404 easily. The following is the detailed procedure to determine the greatest common factor of fractions 730/404, 978/501.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 730/404,978/501?

Given fractions are 730/404,978/501

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 730/404,978/501, numerators are 730,978

Denominators are 404,501

The GCF of 730,978 is 2 .

LCM of 404,501 is 202404.

The greatest common factor of 730/404,978/501 = [GCF of 730,978]/[LCM of 404,501]= 2/202404

Therefore, the GCF of 730/404,978/501 is 2/202404.

Greatest Common Factor of 730,978

To find the highest common factor of 730,978, we have to find the factors of both numbers and list the highest common factor.

The factors of 730 are 1, 2, 5, 10, 73, 146, 365, 730

The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978

The HCF of 730,978 is 2.

Lets's calculate GCF of 730,978

Greatest Common Factor (GCF) of 730,978 By Common Division

2	730, 978
	365, 489

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 730,978 By Matching Biggest Common Factor Method

Now, list down the factors of 730

1,2,5,10,73,146,365,730

Now, list down the factors of 978

1,2,3,6,163,326,489,978

Greatest Common Factor

We found the factors 730,978 . The biggest common factor number is the GCF number.
So the greatest common factor 730,978 is 2.

Lets's calculate LCM of 404,501

Lowest Common Multiple of 404,501 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 202404

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/202404

Therefore, the GCF of Fractions 730/404,978/501 is 2/202404

Least Common Multiple of 404,501 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 404,501 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(404,501) = 1

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

GCF(404,501) x common factors =1 x 1 = 1

LCM(404,501) = ( 404 × 501 ) / 1

LCM(404,501) = 202404 / 1

LCM(404,501) = 202404

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FAQs on GCF of Fractions of 730/404, 978/501

1. What is the HCF of 730,978?

The HCF of 730,978 is 2

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 730/404, 978/501?

Answer: GCF of Numerators as per given numbers 730/404, 978/501 is

GCF of Numerators i.e. for 730,978 is 2

LCM of denominators i.e. for 404,501 is 202404.

Thus, GCF of Fractions is 2/202404.Finally, GCF of Fractions for 730/404, 978/501 is 2/202404.