Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 98/78,68/83,75/97,14/20
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 98,68,75,14
Greatest Common Factor of Numerators i.e. GCF of 98,68,75,14 is 1 .
LCM of Denominators means LCM of 78,83,97,20 as per the given fractions.
LCM of 78,83,97,20 is 6279780 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 98,68,75,14
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 98
List of positive integer factors of 98 that divides 98 without a remainder.
1,2,7,14,49,98
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 75
List of positive integer factors of 75 that divides 75 without a remainder.
1,3,5,15,25,75
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Greatest Common Factor
We found the factors 98,68,75,14 . The biggest common factor number is the GCF number.
So the greatest common factor 98,68,75,14 is 1.
Lets's calculate LCM of 78,83,97,20
2 | 78, 83, 97, 20 |
39, 83, 97, 10 |
∴ So the LCM of the given numbers is 2 x 39 x 83 x 97 x 10 = 6279780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6279780
Therefore, the GCF of Fractions 98/78,68/83,75/97,14/20 is 1/6279780
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 78,83,97,20 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,83,97,20) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(78,83,97,20) x common factors =1 x 2 = 2
LCM(78,83,97,20) = ( 78 × 83 × 97 × 20 ) / 2
LCM(78,83,97,20) = 12559560 / 2
LCM(78,83,97,20) = 6279780
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 98/78, 68/83, 75/97, 14/20?
Answer: GCF of Numerators as per given numbers 98/78, 68/83, 75/97, 14/20 is
GCF of Numerators i.e. for 98,68,75,14 is 1
LCM of denominators i.e. for 78,83,97,20 is 6279780.
Thus, GCF of Fractions is 1/6279780.Finally, GCF of Fractions for 98/78, 68/83, 75/97, 14/20 is 1/6279780.