Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 166/60,209/14,267/16
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 166,209,267
Greatest Common Factor of Numerators i.e. GCF of 166,209,267 is 1 .
LCM of Denominators means LCM of 60,14,16 as per the given fractions.
LCM of 60,14,16 is 1680 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 166,209,267
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 166
List of positive integer factors of 166 that divides 166 without a remainder.
1,2,83,166
Factors of 209
List of positive integer factors of 209 that divides 209 without a remainder.
1,11,19,209
Factors of 267
List of positive integer factors of 267 that divides 267 without a remainder.
1,3,89,267
Greatest Common Factor
We found the factors 166,209,267 . The biggest common factor number is the GCF number.
So the greatest common factor 166,209,267 is 1.
Lets's calculate LCM of 60,14,16
2 | 60, 14, 16 |
2 | 30, 7, 8 |
15, 7, 4 |
∴ So the LCM of the given numbers is 2 x 2 x 15 x 7 x 4 = 1680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1680
Therefore, the GCF of Fractions 166/60,209/14,267/16 is 1/1680
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 60,14,16 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,14,16) = 2
common factors(in case of two or more numbers have common factors) = 4
GCF(60,14,16) x common factors =2 x 4 = 8
LCM(60,14,16) = ( 60 × 14 × 16 ) / 8
LCM(60,14,16) = 13440 / 8
LCM(60,14,16) = 1680
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 166/60, 209/14, 267/16?
Answer: GCF of Numerators as per given numbers 166/60, 209/14, 267/16 is
GCF of Numerators i.e. for 166,209,267 is 1
LCM of denominators i.e. for 60,14,16 is 1680.
Thus, GCF of Fractions is 1/1680.Finally, GCF of Fractions for 166/60, 209/14, 267/16 is 1/1680.