GCF of 860/320, 6180/109
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 860/320, 6180/109 i.e 20/34880 easily. The following is the detailed procedure to determine the greatest common factor of fractions 860/320, 6180/109.
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 860/320,6180/109?
Given fractions are 860/320,6180/109
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 860/320,6180/109, numerators are 860,6180
Denominators are 320,109
The GCF of 860,6180 is 20 .
LCM of 320,109 is 34880.
The greatest common factor of 860/320,6180/109 = [GCF of 860,6180]/[LCM of 320,109]= 20/34880
Therefore, the GCF of 860/320,6180/109 is 20/34880.
To find the highest common factor of 860,6180, we have to find the factors of both numbers and list the highest common factor.
The factors of 860 are 1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860
The factors of 6180 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 103, 206, 309, 412, 515, 618, 1030, 1236, 1545, 2060, 3090, 6180
The HCF of 860,6180 is 20.
Lets's calculate GCF of 860,6180
| 2 | 860, 6180 |
| 2 | 430, 3090 |
| 5 | 215, 1545 |
| 43, 309 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 860,6180 By Matching Biggest Common Factor Method
Now, list down the factors of 860
:1,2,4,5,10,20,43,86,172,215,430,860
Now, list down the factors of 6180
:1,2,3,4,5,6,10,12,15,20,30,60,103,206,309,412,515,618,1030,1236,1545,2060,3090,6180
Greatest Common Factor
We found the factors 860,6180 . The biggest common factor number is the GCF number.
So the greatest common factor 860,6180 is 20.
Lets's calculate LCM of 320,109
Given numbers has no common factors except 1. So, there LCM is their product i.e 34880
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/34880
Therefore, the GCF of Fractions 860/320,6180/109 is 20/34880
Least Common Multiple of 320,109 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 320,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,109) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(320,109) x common factors =1 x 1 = 1
LCM(320,109) = ( 320 × 109 ) / 1
LCM(320,109) = 34880 / 1
LCM(320,109) = 34880
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 860/320, 6180/109
1. What is the HCF of 860,6180?
The HCF of 860,6180 is 20
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 860/320, 6180/109?
Answer: GCF of Numerators as per given numbers 860/320, 6180/109 is
GCF of Numerators i.e. for 860,6180 is 20
LCM of denominators i.e. for 320,109 is 34880.
Thus, GCF of Fractions is 20/34880.Finally, GCF of Fractions for 860/320, 6180/109 is 20/34880.