Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/27,22/72,266/735
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 14,22,266
Greatest Common Factor of Numerators i.e. GCF of 14,22,266 is 2 .
LCM of Denominators means LCM of 27,72,735 as per the given fractions.
LCM of 27,72,735 is 52920 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 14,22,266
2 | 14, 22, 266 |
7, 11, 133 |
∴ So the GCF of the given numbers is 2 = 2
Factors of 14
List of positive integer factors of 14 that divides 14 without a remainder.
1,2,7,14
Factors of 22
List of positive integer factors of 22 that divides 22 without a remainder.
1,2,11,22
Factors of 266
List of positive integer factors of 266 that divides 266 without a remainder.
1,2,7,14,19,38,133,266
Greatest Common Factor
We found the factors 14,22,266 . The biggest common factor number is the GCF number.
So the greatest common factor 14,22,266 is 2.
Lets's calculate LCM of 27,72,735
3 | 27, 72, 735 |
3 | 9, 24, 245 |
3, 8, 245 |
∴ So the LCM of the given numbers is 3 x 3 x 3 x 8 x 245 = 52920
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/52920
Therefore, the GCF of Fractions 14/27,22/72,266/735 is 2/52920
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 27,72,735 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,72,735) = 3
common factors(in case of two or more numbers have common factors) = 9
GCF(27,72,735) x common factors =3 x 9 = 27
LCM(27,72,735) = ( 27 × 72 × 735 ) / 27
LCM(27,72,735) = 1428840 / 27
LCM(27,72,735) = 52920
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 14/27, 22/72, 266/735?
Answer: GCF of Numerators as per given numbers 14/27, 22/72, 266/735 is
GCF of Numerators i.e. for 14,22,266 is 2
LCM of denominators i.e. for 27,72,735 is 52920.
Thus, GCF of Fractions is 2/52920.Finally, GCF of Fractions for 14/27, 22/72, 266/735 is 2/52920.