Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 8/20,640/35,822/60
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 8,640,822
Greatest Common Factor of Numerators i.e. GCF of 8,640,822 is 2 .
LCM of Denominators means LCM of 20,35,60 as per the given fractions.
LCM of 20,35,60 is 420 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 8,640,822
2 | 8, 640, 822 |
4, 320, 411 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 8
List of positive integer factors of 8 that divides 8 without a remainder.
1,2,4,8
Factors of 640
List of positive integer factors of 640 that divides 640 without a remainder.
1,2,4,5,8,10,16,20,32,40,64,80,128,160,320,640
Factors of 822
List of positive integer factors of 822 that divides 822 without a remainder.
1,2,3,6,137,274,411,822
Greatest Common Factor
We found the factors 8,640,822 . The biggest common factor number is the GCF number.
So the greatest common factor 8,640,822 is 2.
Lets's calculate LCM of 20,35,60
2 | 20, 35, 60 |
2 | 10, 35, 30 |
5 | 5, 35, 15 |
1, 7, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 1 x 7 x 3 = 420
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/420
Therefore, the GCF of Fractions 8/20,640/35,822/60 is 2/420
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 20,35,60 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(20,35,60) = 5
common factors(in case of two or more numbers have common factors) = 20
GCF(20,35,60) x common factors =5 x 20 = 100
LCM(20,35,60) = ( 20 × 35 × 60 ) / 100
LCM(20,35,60) = 42000 / 100
LCM(20,35,60) = 420
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 8/20, 640/35, 822/60?
Answer: GCF of Numerators as per given numbers 8/20, 640/35, 822/60 is
GCF of Numerators i.e. for 8,640,822 is 2
LCM of denominators i.e. for 20,35,60 is 420.
Thus, GCF of Fractions is 2/420.Finally, GCF of Fractions for 8/20, 640/35, 822/60 is 2/420.