GCF of 8600/746, 8160/409
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8600/746, 8160/409 i.e 40/305114 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8600/746, 8160/409.
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 8600/746,8160/409?
Given fractions are 8600/746,8160/409
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 8600/746,8160/409, numerators are 8600,8160
Denominators are 746,409
The GCF of 8600,8160 is 40 .
LCM of 746,409 is 305114.
The greatest common factor of 8600/746,8160/409 = [GCF of 8600,8160]/[LCM of 746,409]= 40/305114
Therefore, the GCF of 8600/746,8160/409 is 40/305114.
To find the highest common factor of 8600,8160, we have to find the factors of both numbers and list the highest common factor.
The factors of 8600 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 43, 50, 86, 100, 172, 200, 215, 344, 430, 860, 1075, 1720, 2150, 4300, 8600
The factors of 8160 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 17, 20, 24, 30, 32, 34, 40, 48, 51, 60, 68, 80, 85, 96, 102, 120, 136, 160, 170, 204, 240, 255, 272, 340, 408, 480, 510, 544, 680, 816, 1020, 1360, 1632, 2040, 2720, 4080, 8160
The HCF of 8600,8160 is 40.
Lets's calculate GCF of 8600,8160
| 2 | 8600, 8160 |
| 2 | 4300, 4080 |
| 2 | 2150, 2040 |
| 5 | 1075, 1020 |
| 215, 204 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 8600,8160 By Matching Biggest Common Factor Method
Now, list down the factors of 8600
:1,2,4,5,8,10,20,25,40,43,50,86,100,172,200,215,344,430,860,1075,1720,2150,4300,8600
Now, list down the factors of 8160
:1,2,3,4,5,6,8,10,12,15,16,17,20,24,30,32,34,40,48,51,60,68,80,85,96,102,120,136,160,170,204,240,255,272,340,408,480,510,544,680,816,1020,1360,1632,2040,2720,4080,8160
Greatest Common Factor
We found the factors 8600,8160 . The biggest common factor number is the GCF number.
So the greatest common factor 8600,8160 is 40.
Lets's calculate LCM of 746,409
Given numbers has no common factors except 1. So, there LCM is their product i.e 305114
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/305114
Therefore, the GCF of Fractions 8600/746,8160/409 is 40/305114
Least Common Multiple of 746,409 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 746,409 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(746,409) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(746,409) x common factors =1 x 1 = 1
LCM(746,409) = ( 746 × 409 ) / 1
LCM(746,409) = 305114 / 1
LCM(746,409) = 305114
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FAQs on GCF of Fractions of 8600/746, 8160/409
1. What is the HCF of 8600,8160?
The HCF of 8600,8160 is 40
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 8600/746, 8160/409?
Answer: GCF of Numerators as per given numbers 8600/746, 8160/409 is
GCF of Numerators i.e. for 8600,8160 is 40
LCM of denominators i.e. for 746,409 is 305114.
Thus, GCF of Fractions is 40/305114.Finally, GCF of Fractions for 8600/746, 8160/409 is 40/305114.