Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 50/16,70/48,29/81,37/210
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 50,70,29,37
Greatest Common Factor of Numerators i.e. GCF of 50,70,29,37 is 1 .
LCM of Denominators means LCM of 16,48,81,210 as per the given fractions.
LCM of 16,48,81,210 is 45360 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 50,70,29,37
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 50
List of positive integer factors of 50 that divides 50 without a remainder.
1,2,5,10,25,50
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 29
List of positive integer factors of 29 that divides 29 without a remainder.
1,29
Factors of 37
List of positive integer factors of 37 that divides 37 without a remainder.
1,37
Greatest Common Factor
We found the factors 50,70,29,37 . The biggest common factor number is the GCF number.
So the greatest common factor 50,70,29,37 is 1.
Lets's calculate LCM of 16,48,81,210
2 | 16, 48, 81, 210 |
2 | 8, 24, 81, 105 |
2 | 4, 12, 81, 105 |
2 | 2, 6, 81, 105 |
3 | 1, 3, 81, 105 |
1, 1, 27, 35 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 1 x 1 x 27 x 35 = 45360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/45360
Therefore, the GCF of Fractions 50/16,70/48,29/81,37/210 is 1/45360
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 16,48,81,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,48,81,210) = 1
common factors(in case of two or more numbers have common factors) = 288
GCF(16,48,81,210) x common factors =1 x 288 = 288
LCM(16,48,81,210) = ( 16 × 48 × 81 × 210 ) / 288
LCM(16,48,81,210) = 13063680 / 288
LCM(16,48,81,210) = 45360
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 50/16, 70/48, 29/81, 37/210?
Answer: GCF of Numerators as per given numbers 50/16, 70/48, 29/81, 37/210 is
GCF of Numerators i.e. for 50,70,29,37 is 1
LCM of denominators i.e. for 16,48,81,210 is 45360.
Thus, GCF of Fractions is 1/45360.Finally, GCF of Fractions for 50/16, 70/48, 29/81, 37/210 is 1/45360.