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GCF of 728/470, 7529/442

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 728/470, 7529/442 i.e 1/103870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/470, 7529/442.

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 728/470,7529/442?

Given fractions are 728/470,7529/442

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 728/470,7529/442, numerators are 728,7529

Denominators are 470,442

The GCF of 728,7529 is 1 .

LCM of 470,442 is 103870.

The greatest common factor of 728/470,7529/442 = [GCF of 728,7529]/[LCM of 470,442]= 1/103870

Therefore, the GCF of 728/470,7529/442 is 1/103870.

Greatest Common Factor of 728,7529

To find the highest common factor of 728,7529, 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 7529 are 1, 7529

The HCF of 728,7529 is 1.

Lets's calculate GCF of 728,7529

Greatest Common Factor (GCF) of 728,7529 By Common Division

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

Greatest Common Factor of 728,7529 By Matching Biggest Common Factor Method

Greatest Common Factor of 728,7529 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 7529

:

1,7529

Greatest Common Factor

We found the factors 728,7529 . The biggest common factor number is the GCF number.
So the greatest common factor 728,7529 is 1.

Lets's calculate LCM of 470,442

Lowest Common Multiple of 470,442 using Common Division

2 470, 442
235, 221

∴ So the LCM of the given numbers is 2 x 235 x 221 = 103870

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/103870

Therefore, the GCF of Fractions 728/470,7529/442 is 1/103870

Least Common Multiple of 470,442 with GCF Formula

Least Common Multiple of 470,442 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 470,442 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(470,442) = 2

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

GCF(470,442) x common factors =2 x 1 = 2

LCM(470,442) = ( 470 × 442 ) / 2

LCM(470,442) = 207740 / 2

LCM(470,442) = 103870


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FAQs on GCF of Fractions of 728/470, 7529/442

1. What is the HCF of 728,7529?

The HCF of 728,7529 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 728/470, 7529/442?

Answer: GCF of Numerators as per given numbers 728/470, 7529/442 is

GCF of Numerators i.e. for 728,7529 is 1

LCM of denominators i.e. for 470,442 is 103870.

Thus, GCF of Fractions is 1/103870.Finally, GCF of Fractions for 728/470, 7529/442 is 1/103870.