Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 61/27,66/21,58/71,814/28
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 61,66,58,814
Greatest Common Factor of Numerators i.e. GCF of 61,66,58,814 is 1 .
LCM of Denominators means LCM of 27,21,71,28 as per the given fractions.
LCM of 27,21,71,28 is 53676 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 61,66,58,814
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Factors of 66
List of positive integer factors of 66 that divides 66 without a remainder.
1,2,3,6,11,22,33,66
Factors of 58
List of positive integer factors of 58 that divides 58 without a remainder.
1,2,29,58
Factors of 814
List of positive integer factors of 814 that divides 814 without a remainder.
1,2,11,22,37,74,407,814
Greatest Common Factor
We found the factors 61,66,58,814 . The biggest common factor number is the GCF number.
So the greatest common factor 61,66,58,814 is 1.
Lets's calculate LCM of 27,21,71,28
3 | 27, 21, 71, 28 |
7 | 9, 7, 71, 28 |
9, 1, 71, 4 |
∴ So the LCM of the given numbers is 3 x 7 x 9 x 1 x 71 x 4 = 53676
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/53676
Therefore, the GCF of Fractions 61/27,66/21,58/71,814/28 is 1/53676
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 27,21,71,28 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,21,71,28) = 1
common factors(in case of two or more numbers have common factors) = 21
GCF(27,21,71,28) x common factors =1 x 21 = 21
LCM(27,21,71,28) = ( 27 × 21 × 71 × 28 ) / 21
LCM(27,21,71,28) = 1127196 / 21
LCM(27,21,71,28) = 53676
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 61/27, 66/21, 58/71, 814/28?
Answer: GCF of Numerators as per given numbers 61/27, 66/21, 58/71, 814/28 is
GCF of Numerators i.e. for 61,66,58,814 is 1
LCM of denominators i.e. for 27,21,71,28 is 53676.
Thus, GCF of Fractions is 1/53676.Finally, GCF of Fractions for 61/27, 66/21, 58/71, 814/28 is 1/53676.