Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 57/42,42/18,71/86,680/81
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 57,42,71,680
Greatest Common Factor of Numerators i.e. GCF of 57,42,71,680 is 1 .
LCM of Denominators means LCM of 42,18,86,81 as per the given fractions.
LCM of 42,18,86,81 is 48762 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 57,42,71,680
∴ 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 42
List of positive integer factors of 42 that divides 42 without a remainder.
1,2,3,6,7,14,21,42
Factors of 71
List of positive integer factors of 71 that divides 71 without a remainder.
1,71
Factors of 680
List of positive integer factors of 680 that divides 680 without a remainder.
1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Greatest Common Factor
We found the factors 57,42,71,680 . The biggest common factor number is the GCF number.
So the greatest common factor 57,42,71,680 is 1.
Lets's calculate LCM of 42,18,86,81
2 | 42, 18, 86, 81 |
3 | 21, 9, 43, 81 |
3 | 7, 3, 43, 27 |
7, 1, 43, 9 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 7 x 1 x 43 x 9 = 48762
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/48762
Therefore, the GCF of Fractions 57/42,42/18,71/86,680/81 is 1/48762
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 42,18,86,81 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,18,86,81) = 1
common factors(in case of two or more numbers have common factors) = 108
GCF(42,18,86,81) x common factors =1 x 108 = 108
LCM(42,18,86,81) = ( 42 × 18 × 86 × 81 ) / 108
LCM(42,18,86,81) = 5266296 / 108
LCM(42,18,86,81) = 48762
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 57/42, 42/18, 71/86, 680/81?
Answer: GCF of Numerators as per given numbers 57/42, 42/18, 71/86, 680/81 is
GCF of Numerators i.e. for 57,42,71,680 is 1
LCM of denominators i.e. for 42,18,86,81 is 48762.
Thus, GCF of Fractions is 1/48762.Finally, GCF of Fractions for 57/42, 42/18, 71/86, 680/81 is 1/48762.