GCF of 415/130, 7680/204
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 415/130, 7680/204 i.e 5/13260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 415/130, 7680/204.
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 415/130,7680/204?
Given fractions are 415/130,7680/204
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 415/130,7680/204, numerators are 415,7680
Denominators are 130,204
The GCF of 415,7680 is 5 .
LCM of 130,204 is 13260.
The greatest common factor of 415/130,7680/204 = [GCF of 415,7680]/[LCM of 130,204]= 5/13260
Therefore, the GCF of 415/130,7680/204 is 5/13260.
To find the highest common factor of 415,7680, we have to find the factors of both numbers and list the highest common factor.
The factors of 415 are 1, 5, 83, 415
The factors of 7680 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 256, 320, 384, 480, 512, 640, 768, 960, 1280, 1536, 1920, 2560, 3840, 7680
The HCF of 415,7680 is 5.
Lets's calculate GCF of 415,7680
| 5 | 415, 7680 |
| 83, 1536 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 415,7680 By Matching Biggest Common Factor Method
Now, list down the factors of 415
:1,5,83,415
Now, list down the factors of 7680
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,128,160,192,240,256,320,384,480,512,640,768,960,1280,1536,1920,2560,3840,7680
Greatest Common Factor
We found the factors 415,7680 . The biggest common factor number is the GCF number.
So the greatest common factor 415,7680 is 5.
Lets's calculate LCM of 130,204
| 2 | 130, 204 |
| 65, 102 |
∴ So the LCM of the given numbers is 2 x 65 x 102 = 13260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/13260
Therefore, the GCF of Fractions 415/130,7680/204 is 5/13260
Least Common Multiple of 130,204 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 130,204 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(130,204) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(130,204) x common factors =2 x 1 = 2
LCM(130,204) = ( 130 × 204 ) / 2
LCM(130,204) = 26520 / 2
LCM(130,204) = 13260
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FAQs on GCF of Fractions of 415/130, 7680/204
1. What is the HCF of 415,7680?
The HCF of 415,7680 is 5
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 415/130, 7680/204?
Answer: GCF of Numerators as per given numbers 415/130, 7680/204 is
GCF of Numerators i.e. for 415,7680 is 5
LCM of denominators i.e. for 130,204 is 13260.
Thus, GCF of Fractions is 5/13260.Finally, GCF of Fractions for 415/130, 7680/204 is 5/13260.