Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 68/420,51/696,627/705
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 68,51,627
Greatest Common Factor of Numerators i.e. GCF of 68,51,627 is 1 .
LCM of Denominators means LCM of 420,696,705 as per the given fractions.
LCM of 420,696,705 is 1144920 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 68,51,627
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 51
List of positive integer factors of 51 that divides 51 without a remainder.
1,3,17,51
Factors of 627
List of positive integer factors of 627 that divides 627 without a remainder.
1,3,11,19,33,57,209,627
Greatest Common Factor
We found the factors 68,51,627 . The biggest common factor number is the GCF number.
So the greatest common factor 68,51,627 is 1.
Lets's calculate LCM of 420,696,705
2 | 420, 696, 705 |
2 | 210, 348, 705 |
3 | 105, 174, 705 |
5 | 35, 58, 235 |
7, 58, 47 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 58 x 47 = 1144920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1144920
Therefore, the GCF of Fractions 68/420,51/696,627/705 is 1/1144920
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 420,696,705 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,696,705) = 3
common factors(in case of two or more numbers have common factors) = 60
GCF(420,696,705) x common factors =3 x 60 = 180
LCM(420,696,705) = ( 420 × 696 × 705 ) / 180
LCM(420,696,705) = 206085600 / 180
LCM(420,696,705) = 1144920
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 68/420, 51/696, 627/705?
Answer: GCF of Numerators as per given numbers 68/420, 51/696, 627/705 is
GCF of Numerators i.e. for 68,51,627 is 1
LCM of denominators i.e. for 420,696,705 is 1144920.
Thus, GCF of Fractions is 1/1144920.Finally, GCF of Fractions for 68/420, 51/696, 627/705 is 1/1144920.