Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 680/2060,780/1109
Formula to find GCF of Fractions is
GCF = GCF of Numerators/LCM of Denominators
As per the formula GCF of Fractions let’s split into two parts and find the GCF of Numerators and LCM of Denominators
In the given fractions GCF of Numerators means GCF of 680,780
Greatest Common Factor of Numerators i.e. GCF of 680,780 is 20 .
LCM of Denominators means LCM of 2060,1109 as per the given fractions.
LCM of 2060,1109 is 2284540 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 680,780
2 | 680, 780 |
2 | 340, 390 |
5 | 170, 195 |
34, 39 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Factors of 680
List of positive integer factors of 680 that divides 680 without a remainder.
1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Factors of 780
List of positive integer factors of 780 that divides 780 without a remainder.
1,2,3,4,5,6,10,12,13,15,20,26,30,39,52,60,65,78,130,156,195,260,390,780
Greatest Common Factor
We found the factors 680,780 . The biggest common factor number is the GCF number.
So the greatest common factor 680,780 is 20.
Lets's calculate LCM of 2060,1109
Given numbers has no common factors except 1. So, there LCM is their product i.e 2284540
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/2284540
Therefore, the GCF of Fractions 680/2060,780/1109 is 20/2284540
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 2060,1109 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(2060,1109) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(2060,1109) x common factors =1 x 1 = 1
LCM(2060,1109) = ( 2060 × 1109 ) / 1
LCM(2060,1109) = 2284540 / 1
LCM(2060,1109) = 2284540
Here are some samples of GCF of Fractions calculations.
Here are some samples of GCF of Fractions calculations.
1. 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.
2. What is the GCF of Fractions for 680/2060, 780/1109?
Answer: GCF of Numerators as per given numbers 680/2060, 780/1109 is
GCF of Numerators i.e. for 680,780 is 20
LCM of denominators i.e. for 2060,1109 is 2284540.
Thus, GCF of Fractions is 20/2284540.Finally, GCF of Fractions for 680/2060, 780/1109 is 20/2284540.