GCF of 130/579, 5760/258
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 130/579, 5760/258 i.e 10/49794 easily. The following is the detailed procedure to determine the greatest common factor of fractions 130/579, 5760/258.
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 130/579,5760/258?
Given fractions are 130/579,5760/258
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 130/579,5760/258, numerators are 130,5760
Denominators are 579,258
The GCF of 130,5760 is 10 .
LCM of 579,258 is 49794.
The greatest common factor of 130/579,5760/258 = [GCF of 130,5760]/[LCM of 579,258]= 10/49794
Therefore, the GCF of 130/579,5760/258 is 10/49794.
To find the highest common factor of 130,5760, we have to find the factors of both numbers and list the highest common factor.
The factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130
The factors of 5760 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760
The HCF of 130,5760 is 10.
Lets's calculate GCF of 130,5760
| 2 | 130, 5760 |
| 5 | 65, 2880 |
| 13, 576 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 130,5760 By Matching Biggest Common Factor Method
Now, list down the factors of 130
:1,2,5,10,13,26,65,130
Now, list down the factors of 5760
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,32,36,40,45,48,60,64,72,80,90,96,120,128,144,160,180,192,240,288,320,360,384,480,576,640,720,960,1152,1440,1920,2880,5760
Greatest Common Factor
We found the factors 130,5760 . The biggest common factor number is the GCF number.
So the greatest common factor 130,5760 is 10.
Lets's calculate LCM of 579,258
| 3 | 579, 258 |
| 193, 86 |
∴ So the LCM of the given numbers is 3 x 193 x 86 = 49794
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/49794
Therefore, the GCF of Fractions 130/579,5760/258 is 10/49794
Least Common Multiple of 579,258 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 579,258 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(579,258) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(579,258) x common factors =3 x 1 = 3
LCM(579,258) = ( 579 × 258 ) / 3
LCM(579,258) = 149382 / 3
LCM(579,258) = 49794
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FAQs on GCF of Fractions of 130/579, 5760/258
1. What is the HCF of 130,5760?
The HCF of 130,5760 is 10
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 130/579, 5760/258?
Answer: GCF of Numerators as per given numbers 130/579, 5760/258 is
GCF of Numerators i.e. for 130,5760 is 10
LCM of denominators i.e. for 579,258 is 49794.
Thus, GCF of Fractions is 10/49794.Finally, GCF of Fractions for 130/579, 5760/258 is 10/49794.