GCF of 8120/343, 5170/3684
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8120/343, 5170/3684 i.e 10/1263612 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8120/343, 5170/3684.
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 8120/343,5170/3684?
Given fractions are 8120/343,5170/3684
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 8120/343,5170/3684, numerators are 8120,5170
Denominators are 343,3684
The GCF of 8120,5170 is 10 .
LCM of 343,3684 is 1263612.
The greatest common factor of 8120/343,5170/3684 = [GCF of 8120,5170]/[LCM of 343,3684]= 10/1263612
Therefore, the GCF of 8120/343,5170/3684 is 10/1263612.
To find the highest common factor of 8120,5170, we have to find the factors of both numbers and list the highest common factor.
The factors of 8120 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 29, 35, 40, 56, 58, 70, 116, 140, 145, 203, 232, 280, 290, 406, 580, 812, 1015, 1160, 1624, 2030, 4060, 8120
The factors of 5170 are 1, 2, 5, 10, 11, 22, 47, 55, 94, 110, 235, 470, 517, 1034, 2585, 5170
The HCF of 8120,5170 is 10.
Lets's calculate GCF of 8120,5170
| 2 | 8120, 5170 |
| 5 | 4060, 2585 |
| 812, 517 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 8120,5170 By Matching Biggest Common Factor Method
Now, list down the factors of 8120
:1,2,4,5,7,8,10,14,20,28,29,35,40,56,58,70,116,140,145,203,232,280,290,406,580,812,1015,1160,1624,2030,4060,8120
Now, list down the factors of 5170
:1,2,5,10,11,22,47,55,94,110,235,470,517,1034,2585,5170
Greatest Common Factor
We found the factors 8120,5170 . The biggest common factor number is the GCF number.
So the greatest common factor 8120,5170 is 10.
Lets's calculate LCM of 343,3684
Given numbers has no common factors except 1. So, there LCM is their product i.e 1263612
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/1263612
Therefore, the GCF of Fractions 8120/343,5170/3684 is 10/1263612
Least Common Multiple of 343,3684 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 343,3684 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(343,3684) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(343,3684) x common factors =1 x 1 = 1
LCM(343,3684) = ( 343 × 3684 ) / 1
LCM(343,3684) = 1263612 / 1
LCM(343,3684) = 1263612
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FAQs on GCF of Fractions of 8120/343, 5170/3684
1. What is the HCF of 8120,5170?
The HCF of 8120,5170 is 10
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 8120/343, 5170/3684?
Answer: GCF of Numerators as per given numbers 8120/343, 5170/3684 is
GCF of Numerators i.e. for 8120,5170 is 10
LCM of denominators i.e. for 343,3684 is 1263612.
Thus, GCF of Fractions is 10/1263612.Finally, GCF of Fractions for 8120/343, 5170/3684 is 10/1263612.