Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 59/12,47/42,12/80,68/360
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 59,47,12,68
Greatest Common Factor of Numerators i.e. GCF of 59,47,12,68 is 1 .
LCM of Denominators means LCM of 12,42,80,360 as per the given fractions.
LCM of 12,42,80,360 is 5040 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 59,47,12,68
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 59
List of positive integer factors of 59 that divides 59 without a remainder.
1,59
Factors of 47
List of positive integer factors of 47 that divides 47 without a remainder.
1,47
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Greatest Common Factor
We found the factors 59,47,12,68 . The biggest common factor number is the GCF number.
So the greatest common factor 59,47,12,68 is 1.
Lets's calculate LCM of 12,42,80,360
2 | 12, 42, 80, 360 |
2 | 6, 21, 40, 180 |
2 | 3, 21, 20, 90 |
3 | 3, 21, 10, 45 |
5 | 1, 7, 10, 15 |
1, 7, 2, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 1 x 7 x 2 x 3 = 5040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5040
Therefore, the GCF of Fractions 59/12,47/42,12/80,68/360 is 1/5040
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 12,42,80,360 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,42,80,360) = 2
common factors(in case of two or more numbers have common factors) = 1440
GCF(12,42,80,360) x common factors =2 x 1440 = 2880
LCM(12,42,80,360) = ( 12 × 42 × 80 × 360 ) / 2880
LCM(12,42,80,360) = 14515200 / 2880
LCM(12,42,80,360) = 5040
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 59/12, 47/42, 12/80, 68/360?
Answer: GCF of Numerators as per given numbers 59/12, 47/42, 12/80, 68/360 is
GCF of Numerators i.e. for 59,47,12,68 is 1
LCM of denominators i.e. for 12,42,80,360 is 5040.
Thus, GCF of Fractions is 1/5040.Finally, GCF of Fractions for 59/12, 47/42, 12/80, 68/360 is 1/5040.