Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 108/205,126/683
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 108,126
Greatest Common Factor of Numerators i.e. GCF of 108,126 is 18 .
LCM of Denominators means LCM of 205,683 as per the given fractions.
LCM of 205,683 is 140015 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 108,126
2 | 108, 126 |
3 | 54, 63 |
3 | 18, 21 |
6, 7 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Factors of 108
List of positive integer factors of 108 that divides 108 without a remainder.
1,2,3,4,6,9,12,18,27,36,54,108
Factors of 126
List of positive integer factors of 126 that divides 126 without a remainder.
1,2,3,6,7,9,14,18,21,42,63,126
Greatest Common Factor
We found the factors 108,126 . The biggest common factor number is the GCF number.
So the greatest common factor 108,126 is 18.
Lets's calculate LCM of 205,683
Given numbers has no common factors except 1. So, there LCM is their product i.e 140015
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/140015
Therefore, the GCF of Fractions 108/205,126/683 is 18/140015
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 205,683 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,683) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(205,683) x common factors =1 x 1 = 1
LCM(205,683) = ( 205 × 683 ) / 1
LCM(205,683) = 140015 / 1
LCM(205,683) = 140015
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 108/205, 126/683?
Answer: GCF of Numerators as per given numbers 108/205, 126/683 is
GCF of Numerators i.e. for 108,126 is 18
LCM of denominators i.e. for 205,683 is 140015.
Thus, GCF of Fractions is 18/140015.Finally, GCF of Fractions for 108/205, 126/683 is 18/140015.