GCF of 8127/416, 7680/8073
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8127/416, 7680/8073 i.e 3/258336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8127/416, 7680/8073.
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 8127/416,7680/8073?
Given fractions are 8127/416,7680/8073
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 8127/416,7680/8073, numerators are 8127,7680
Denominators are 416,8073
The GCF of 8127,7680 is 3 .
LCM of 416,8073 is 258336.
The greatest common factor of 8127/416,7680/8073 = [GCF of 8127,7680]/[LCM of 416,8073]= 3/258336
Therefore, the GCF of 8127/416,7680/8073 is 3/258336.
To find the highest common factor of 8127,7680, we have to find the factors of both numbers and list the highest common factor.
The factors of 8127 are 1, 3, 7, 9, 21, 27, 43, 63, 129, 189, 301, 387, 903, 1161, 2709, 8127
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 8127,7680 is 3.
Lets's calculate GCF of 8127,7680
| 3 | 8127, 7680 |
| 2709, 2560 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 8127,7680 By Matching Biggest Common Factor Method
Now, list down the factors of 8127
:1,3,7,9,21,27,43,63,129,189,301,387,903,1161,2709,8127
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 8127,7680 . The biggest common factor number is the GCF number.
So the greatest common factor 8127,7680 is 3.
Lets's calculate LCM of 416,8073
| 13 | 416, 8073 |
| 32, 621 |
∴ So the LCM of the given numbers is 13 x 32 x 621 = 258336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/258336
Therefore, the GCF of Fractions 8127/416,7680/8073 is 3/258336
Least Common Multiple of 416,8073 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 416,8073 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(416,8073) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(416,8073) x common factors =13 x 1 = 13
LCM(416,8073) = ( 416 × 8073 ) / 13
LCM(416,8073) = 3358368 / 13
LCM(416,8073) = 258336
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FAQs on GCF of Fractions of 8127/416, 7680/8073
1. What is the HCF of 8127,7680?
The HCF of 8127,7680 is 3
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 8127/416, 7680/8073?
Answer: GCF of Numerators as per given numbers 8127/416, 7680/8073 is
GCF of Numerators i.e. for 8127,7680 is 3
LCM of denominators i.e. for 416,8073 is 258336.
Thus, GCF of Fractions is 3/258336.Finally, GCF of Fractions for 8127/416, 7680/8073 is 3/258336.