Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 57/12,96/72,61/59,164/24
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 57,96,61,164
Greatest Common Factor of Numerators i.e. GCF of 57,96,61,164 is 1 .
LCM of Denominators means LCM of 12,72,59,24 as per the given fractions.
LCM of 12,72,59,24 is 4248 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 57,96,61,164
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 57
List of positive integer factors of 57 that divides 57 without a remainder.
1,3,19,57
Factors of 96
List of positive integer factors of 96 that divides 96 without a remainder.
1,2,3,4,6,8,12,16,24,32,48,96
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Factors of 164
List of positive integer factors of 164 that divides 164 without a remainder.
1,2,4,41,82,164
Greatest Common Factor
We found the factors 57,96,61,164 . The biggest common factor number is the GCF number.
So the greatest common factor 57,96,61,164 is 1.
Lets's calculate LCM of 12,72,59,24
2 | 12, 72, 59, 24 |
2 | 6, 36, 59, 12 |
2 | 3, 18, 59, 6 |
3 | 3, 9, 59, 3 |
1, 1, 59, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 1 x 1 x 59 x 3 = 4248
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4248
Therefore, the GCF of Fractions 57/12,96/72,61/59,164/24 is 1/4248
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 12,72,59,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,72,59,24) = 1
common factors(in case of two or more numbers have common factors) = 288
GCF(12,72,59,24) x common factors =1 x 288 = 288
LCM(12,72,59,24) = ( 12 × 72 × 59 × 24 ) / 288
LCM(12,72,59,24) = 1223424 / 288
LCM(12,72,59,24) = 4248
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 57/12, 96/72, 61/59, 164/24?
Answer: GCF of Numerators as per given numbers 57/12, 96/72, 61/59, 164/24 is
GCF of Numerators i.e. for 57,96,61,164 is 1
LCM of denominators i.e. for 12,72,59,24 is 4248.
Thus, GCF of Fractions is 1/4248.Finally, GCF of Fractions for 57/12, 96/72, 61/59, 164/24 is 1/4248.