How to Find GCF of 760/470, 513/208?

GCF of 760/470, 513/208

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 760/470, 513/208 i.e 19/48880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 760/470, 513/208.

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 760/470,513/208?

Given fractions are 760/470,513/208

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 760/470,513/208, numerators are 760,513

Denominators are 470,208

The GCF of 760,513 is 19 .

LCM of 470,208 is 48880.

The greatest common factor of 760/470,513/208 = [GCF of 760,513]/[LCM of 470,208]= 19/48880

Therefore, the GCF of 760/470,513/208 is 19/48880.

Greatest Common Factor of 760,513

To find the highest common factor of 760,513, we have to find the factors of both numbers and list the highest common factor.

The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760

The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513

The HCF of 760,513 is 19.

Lets's calculate GCF of 760,513

Greatest Common Factor (GCF) of 760,513 By Common Division

19	760, 513
	40, 27

∴ So the GCF of the given numbers is 19 = 19

Greatest Common Factor of 760,513 By Matching Biggest Common Factor Method

Now, list down the factors of 760

1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760

Now, list down the factors of 513

1,3,9,19,27,57,171,513

Greatest Common Factor

We found the factors 760,513 . The biggest common factor number is the GCF number.
So the greatest common factor 760,513 is 19.

Lets's calculate LCM of 470,208

Lowest Common Multiple of 470,208 using Common Division

2	470, 208
	235, 104

∴ So the LCM of the given numbers is 2 x 235 x 104 = 48880

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 19/48880

Therefore, the GCF of Fractions 760/470,513/208 is 19/48880

Least Common Multiple of 470,208 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 470,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(470,208) = 2

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

GCF(470,208) x common factors =2 x 1 = 2

LCM(470,208) = ( 470 × 208 ) / 2

LCM(470,208) = 97760 / 2

LCM(470,208) = 48880

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FAQs on GCF of Fractions of 760/470, 513/208

1. What is the HCF of 760,513?

The HCF of 760,513 is 19

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 760/470, 513/208?

Answer: GCF of Numerators as per given numbers 760/470, 513/208 is

GCF of Numerators i.e. for 760,513 is 19

LCM of denominators i.e. for 470,208 is 48880.

Thus, GCF of Fractions is 19/48880.Finally, GCF of Fractions for 760/470, 513/208 is 19/48880.