Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/66,57/54,686/243
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 77,57,686
Greatest Common Factor of Numerators i.e. GCF of 77,57,686 is 1 .
LCM of Denominators means LCM of 66,54,243 as per the given fractions.
LCM of 66,54,243 is 5346 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 77,57,686
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 77
List of positive integer factors of 77 that divides 77 without a remainder.
1,7,11,77
Factors of 57
List of positive integer factors of 57 that divides 57 without a remainder.
1,3,19,57
Factors of 686
List of positive integer factors of 686 that divides 686 without a remainder.
1,2,7,14,49,98,343,686
Greatest Common Factor
We found the factors 77,57,686 . The biggest common factor number is the GCF number.
So the greatest common factor 77,57,686 is 1.
Lets's calculate LCM of 66,54,243
2 | 66, 54, 243 |
3 | 33, 27, 243 |
3 | 11, 9, 81 |
3 | 11, 3, 27 |
11, 1, 9 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 3 x 11 x 1 x 9 = 5346
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5346
Therefore, the GCF of Fractions 77/66,57/54,686/243 is 1/5346
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 66,54,243 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(66,54,243) = 3
common factors(in case of two or more numbers have common factors) = 54
GCF(66,54,243) x common factors =3 x 54 = 162
LCM(66,54,243) = ( 66 × 54 × 243 ) / 162
LCM(66,54,243) = 866052 / 162
LCM(66,54,243) = 5346
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 77/66, 57/54, 686/243?
Answer: GCF of Numerators as per given numbers 77/66, 57/54, 686/243 is
GCF of Numerators i.e. for 77,57,686 is 1
LCM of denominators i.e. for 66,54,243 is 5346.
Thus, GCF of Fractions is 1/5346.Finally, GCF of Fractions for 77/66, 57/54, 686/243 is 1/5346.