Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 35/106,154/262
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 35,154
Greatest Common Factor of Numerators i.e. GCF of 35,154 is 7 .
LCM of Denominators means LCM of 106,262 as per the given fractions.
LCM of 106,262 is 13886 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 35,154
7 | 35, 154 |
5, 22 |
∴ So the GCF of the given numbers is 7 = 7
Factors of 35
List of positive integer factors of 35 that divides 35 without a remainder.
1,5,7,35
Factors of 154
List of positive integer factors of 154 that divides 154 without a remainder.
1,2,7,11,14,22,77,154
Greatest Common Factor
We found the factors 35,154 . The biggest common factor number is the GCF number.
So the greatest common factor 35,154 is 7.
Lets's calculate LCM of 106,262
2 | 106, 262 |
53, 131 |
∴ So the LCM of the given numbers is 2 x 53 x 131 = 13886
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/13886
Therefore, the GCF of Fractions 35/106,154/262 is 7/13886
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 106,262 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,262) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(106,262) x common factors =2 x 1 = 2
LCM(106,262) = ( 106 × 262 ) / 2
LCM(106,262) = 27772 / 2
LCM(106,262) = 13886
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 35/106, 154/262?
Answer: GCF of Numerators as per given numbers 35/106, 154/262 is
GCF of Numerators i.e. for 35,154 is 7
LCM of denominators i.e. for 106,262 is 13886.
Thus, GCF of Fractions is 7/13886.Finally, GCF of Fractions for 35/106, 154/262 is 7/13886.