How to Find GCF of 728/331, 9451/258?

GCF of 728/331, 9451/258

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 728/331, 9451/258 i.e 13/85398 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/331, 9451/258.

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 728/331,9451/258?

Given fractions are 728/331,9451/258

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 728/331,9451/258, numerators are 728,9451

Denominators are 331,258

The GCF of 728,9451 is 13 .

LCM of 331,258 is 85398.

The greatest common factor of 728/331,9451/258 = [GCF of 728,9451]/[LCM of 331,258]= 13/85398

Therefore, the GCF of 728/331,9451/258 is 13/85398.

Greatest Common Factor of 728,9451

To find the highest common factor of 728,9451, we have to find the factors of both numbers and list the highest common factor.

The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728

The factors of 9451 are 1, 13, 727, 9451

The HCF of 728,9451 is 13.

Lets's calculate GCF of 728,9451

Greatest Common Factor (GCF) of 728,9451 By Common Division

13	728, 9451
	56, 727

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 728,9451 By Matching Biggest Common Factor Method

Now, list down the factors of 728

1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728

Now, list down the factors of 9451

1,13,727,9451

Greatest Common Factor

We found the factors 728,9451 . The biggest common factor number is the GCF number.
So the greatest common factor 728,9451 is 13.

Lets's calculate LCM of 331,258

Lowest Common Multiple of 331,258 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 85398

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/85398

Therefore, the GCF of Fractions 728/331,9451/258 is 13/85398

Least Common Multiple of 331,258 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 331,258 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(331,258) = 1

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

GCF(331,258) x common factors =1 x 1 = 1

LCM(331,258) = ( 331 × 258 ) / 1

LCM(331,258) = 85398 / 1

LCM(331,258) = 85398

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FAQs on GCF of Fractions of 728/331, 9451/258

1. What is the HCF of 728,9451?

The HCF of 728,9451 is 13

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 728/331, 9451/258?

Answer: GCF of Numerators as per given numbers 728/331, 9451/258 is

GCF of Numerators i.e. for 728,9451 is 13

LCM of denominators i.e. for 331,258 is 85398.

Thus, GCF of Fractions is 13/85398.Finally, GCF of Fractions for 728/331, 9451/258 is 13/85398.