Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 80/19,28/57,40/78,25/210
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 80,28,40,25
Greatest Common Factor of Numerators i.e. GCF of 80,28,40,25 is 1 .
LCM of Denominators means LCM of 19,57,78,210 as per the given fractions.
LCM of 19,57,78,210 is 51870 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 80,28,40,25
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 80
List of positive integer factors of 80 that divides 80 without a remainder.
1,2,4,5,8,10,16,20,40,80
Factors of 28
List of positive integer factors of 28 that divides 28 without a remainder.
1,2,4,7,14,28
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1,5,25
Greatest Common Factor
We found the factors 80,28,40,25 . The biggest common factor number is the GCF number.
So the greatest common factor 80,28,40,25 is 1.
Lets's calculate LCM of 19,57,78,210
2 | 19, 57, 78, 210 |
3 | 19, 57, 39, 105 |
19 | 19, 19, 13, 35 |
1, 1, 13, 35 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 1 x 1 x 13 x 35 = 51870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/51870
Therefore, the GCF of Fractions 80/19,28/57,40/78,25/210 is 1/51870
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 19,57,78,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(19,57,78,210) = 1
common factors(in case of two or more numbers have common factors) = 342
GCF(19,57,78,210) x common factors =1 x 342 = 342
LCM(19,57,78,210) = ( 19 × 57 × 78 × 210 ) / 342
LCM(19,57,78,210) = 17739540 / 342
LCM(19,57,78,210) = 51870
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 80/19, 28/57, 40/78, 25/210?
Answer: GCF of Numerators as per given numbers 80/19, 28/57, 40/78, 25/210 is
GCF of Numerators i.e. for 80,28,40,25 is 1
LCM of denominators i.e. for 19,57,78,210 is 51870.
Thus, GCF of Fractions is 1/51870.Finally, GCF of Fractions for 80/19, 28/57, 40/78, 25/210 is 1/51870.