GCF of 8610/148, 7680/6832
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8610/148, 7680/6832 i.e 30/252784 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8610/148, 7680/6832.
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 8610/148,7680/6832?
Given fractions are 8610/148,7680/6832
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 8610/148,7680/6832, numerators are 8610,7680
Denominators are 148,6832
The GCF of 8610,7680 is 30 .
LCM of 148,6832 is 252784.
The greatest common factor of 8610/148,7680/6832 = [GCF of 8610,7680]/[LCM of 148,6832]= 30/252784
Therefore, the GCF of 8610/148,7680/6832 is 30/252784.
To find the highest common factor of 8610,7680, we have to find the factors of both numbers and list the highest common factor.
The factors of 8610 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 41, 42, 70, 82, 105, 123, 205, 210, 246, 287, 410, 574, 615, 861, 1230, 1435, 1722, 2870, 4305, 8610
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 8610,7680 is 30.
Lets's calculate GCF of 8610,7680
| 2 | 8610, 7680 |
| 3 | 4305, 3840 |
| 5 | 1435, 1280 |
| 287, 256 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 8610,7680 By Matching Biggest Common Factor Method
Now, list down the factors of 8610
:1,2,3,5,6,7,10,14,15,21,30,35,41,42,70,82,105,123,205,210,246,287,410,574,615,861,1230,1435,1722,2870,4305,8610
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 8610,7680 . The biggest common factor number is the GCF number.
So the greatest common factor 8610,7680 is 30.
Lets's calculate LCM of 148,6832
| 2 | 148, 6832 |
| 2 | 74, 3416 |
| 37, 1708 |
∴ So the LCM of the given numbers is 2 x 2 x 37 x 1708 = 252784
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/252784
Therefore, the GCF of Fractions 8610/148,7680/6832 is 30/252784
Least Common Multiple of 148,6832 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 148,6832 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(148,6832) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(148,6832) x common factors =4 x 1 = 4
LCM(148,6832) = ( 148 × 6832 ) / 4
LCM(148,6832) = 1011136 / 4
LCM(148,6832) = 252784
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FAQs on GCF of Fractions of 8610/148, 7680/6832
1. What is the HCF of 8610,7680?
The HCF of 8610,7680 is 30
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 8610/148, 7680/6832?
Answer: GCF of Numerators as per given numbers 8610/148, 7680/6832 is
GCF of Numerators i.e. for 8610,7680 is 30
LCM of denominators i.e. for 148,6832 is 252784.
Thus, GCF of Fractions is 30/252784.Finally, GCF of Fractions for 8610/148, 7680/6832 is 30/252784.