Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/565,76/220,230/340
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 78,76,230
Greatest Common Factor of Numerators i.e. GCF of 78,76,230 is 2 .
LCM of Denominators means LCM of 565,220,340 as per the given fractions.
LCM of 565,220,340 is 422620 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 78,76,230
2 | 78, 76, 230 |
39, 38, 115 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 78
List of positive integer factors of 78 that divides 78 without a remainder.
1,2,3,6,13,26,39,78
Factors of 76
List of positive integer factors of 76 that divides 76 without a remainder.
1,2,4,19,38,76
Factors of 230
List of positive integer factors of 230 that divides 230 without a remainder.
1,2,5,10,23,46,115,230
Greatest Common Factor
We found the factors 78,76,230 . The biggest common factor number is the GCF number.
So the greatest common factor 78,76,230 is 2.
Lets's calculate LCM of 565,220,340
2 | 565, 220, 340 |
2 | 565, 110, 170 |
5 | 565, 55, 85 |
113, 11, 17 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 113 x 11 x 17 = 422620
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/422620
Therefore, the GCF of Fractions 78/565,76/220,230/340 is 2/422620
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 565,220,340 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(565,220,340) = 5
common factors(in case of two or more numbers have common factors) = 20
GCF(565,220,340) x common factors =5 x 20 = 100
LCM(565,220,340) = ( 565 × 220 × 340 ) / 100
LCM(565,220,340) = 42262000 / 100
LCM(565,220,340) = 422620
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 78/565, 76/220, 230/340?
Answer: GCF of Numerators as per given numbers 78/565, 76/220, 230/340 is
GCF of Numerators i.e. for 78,76,230 is 2
LCM of denominators i.e. for 565,220,340 is 422620.
Thus, GCF of Fractions is 2/422620.Finally, GCF of Fractions for 78/565, 76/220, 230/340 is 2/422620.