Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 142/60,250/67,412/830
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 142,250,412
Greatest Common Factor of Numerators i.e. GCF of 142,250,412 is 2 .
LCM of Denominators means LCM of 60,67,830 as per the given fractions.
LCM of 60,67,830 is 333660 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 142,250,412
2 | 142, 250, 412 |
71, 125, 206 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 142
List of positive integer factors of 142 that divides 142 without a remainder.
1,2,71,142
Factors of 250
List of positive integer factors of 250 that divides 250 without a remainder.
1,2,5,10,25,50,125,250
Factors of 412
List of positive integer factors of 412 that divides 412 without a remainder.
1,2,4,103,206,412
Greatest Common Factor
We found the factors 142,250,412 . The biggest common factor number is the GCF number.
So the greatest common factor 142,250,412 is 2.
Lets's calculate LCM of 60,67,830
2 | 60, 67, 830 |
5 | 30, 67, 415 |
6, 67, 83 |
∴ So the LCM of the given numbers is 2 x 5 x 6 x 67 x 83 = 333660
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/333660
Therefore, the GCF of Fractions 142/60,250/67,412/830 is 2/333660
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 60,67,830 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,67,830) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(60,67,830) x common factors =1 x 10 = 10
LCM(60,67,830) = ( 60 × 67 × 830 ) / 10
LCM(60,67,830) = 3336600 / 10
LCM(60,67,830) = 333660
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 142/60, 250/67, 412/830?
Answer: GCF of Numerators as per given numbers 142/60, 250/67, 412/830 is
GCF of Numerators i.e. for 142,250,412 is 2
LCM of denominators i.e. for 60,67,830 is 333660.
Thus, GCF of Fractions is 2/333660.Finally, GCF of Fractions for 142/60, 250/67, 412/830 is 2/333660.