GCF of 2074/873, 5760/378
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2074/873, 5760/378 i.e 2/36666 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2074/873, 5760/378.
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 2074/873,5760/378?
Given fractions are 2074/873,5760/378
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 2074/873,5760/378, numerators are 2074,5760
Denominators are 873,378
The GCF of 2074,5760 is 2 .
LCM of 873,378 is 36666.
The greatest common factor of 2074/873,5760/378 = [GCF of 2074,5760]/[LCM of 873,378]= 2/36666
Therefore, the GCF of 2074/873,5760/378 is 2/36666.
To find the highest common factor of 2074,5760, we have to find the factors of both numbers and list the highest common factor.
The factors of 2074 are 1, 2, 17, 34, 61, 122, 1037, 2074
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 2074,5760 is 2.
Lets's calculate GCF of 2074,5760
| 2 | 2074, 5760 |
| 1037, 2880 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2074,5760 By Matching Biggest Common Factor Method
Now, list down the factors of 2074
:1,2,17,34,61,122,1037,2074
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 2074,5760 . The biggest common factor number is the GCF number.
So the greatest common factor 2074,5760 is 2.
Lets's calculate LCM of 873,378
| 3 | 873, 378 |
| 3 | 291, 126 |
| 97, 42 |
∴ So the LCM of the given numbers is 3 x 3 x 97 x 42 = 36666
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/36666
Therefore, the GCF of Fractions 2074/873,5760/378 is 2/36666
Least Common Multiple of 873,378 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 873,378 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(873,378) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(873,378) x common factors =9 x 1 = 9
LCM(873,378) = ( 873 × 378 ) / 9
LCM(873,378) = 329994 / 9
LCM(873,378) = 36666
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FAQs on GCF of Fractions of 2074/873, 5760/378
1. What is the HCF of 2074,5760?
The HCF of 2074,5760 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 2074/873, 5760/378?
Answer: GCF of Numerators as per given numbers 2074/873, 5760/378 is
GCF of Numerators i.e. for 2074,5760 is 2
LCM of denominators i.e. for 873,378 is 36666.
Thus, GCF of Fractions is 2/36666.Finally, GCF of Fractions for 2074/873, 5760/378 is 2/36666.