Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 78/60,61/98,70/51,66/48
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 78,61,70,66
Greatest Common Factor of Numerators i.e. GCF of 78,61,70,66 is 1 .
LCM of Denominators means LCM of 60,98,51,48 as per the given fractions.
LCM of 60,98,51,48 is 199920 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 78,61,70,66
∴ So GCF of numbers is 1 because of no common factors present between them.
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 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Factors of 70
List of positive integer factors of 70 that divides 70 without a remainder.
1,2,5,7,10,14,35,70
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Greatest Common Factor
We found the factors 78,61,70,66 . The biggest common factor number is the GCF number.
So the greatest common factor 78,61,70,66 is 1.
Lets's calculate LCM of 60,98,51,48
2 | 60, 98, 51, 48 |
2 | 30, 49, 51, 24 |
3 | 15, 49, 51, 12 |
5, 49, 17, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 49 x 17 x 4 = 199920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/199920
Therefore, the GCF of Fractions 78/60,61/98,70/51,66/48 is 1/199920
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 60,98,51,48 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,98,51,48) = 1
common factors(in case of two or more numbers have common factors) = 72
GCF(60,98,51,48) x common factors =1 x 72 = 72
LCM(60,98,51,48) = ( 60 × 98 × 51 × 48 ) / 72
LCM(60,98,51,48) = 14394240 / 72
LCM(60,98,51,48) = 199920
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 78/60, 61/98, 70/51, 66/48?
Answer: GCF of Numerators as per given numbers 78/60, 61/98, 70/51, 66/48 is
GCF of Numerators i.e. for 78,61,70,66 is 1
LCM of denominators i.e. for 60,98,51,48 is 199920.
Thus, GCF of Fractions is 1/199920.Finally, GCF of Fractions for 78/60, 61/98, 70/51, 66/48 is 1/199920.