Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 81/18,90/21,85/42,59/687
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 81,90,85,59
Greatest Common Factor of Numerators i.e. GCF of 81,90,85,59 is 1 .
LCM of Denominators means LCM of 18,21,42,687 as per the given fractions.
LCM of 18,21,42,687 is 28854 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 81,90,85,59
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 81
List of positive integer factors of 81 that divides 81 without a remainder.
1,3,9,27,81
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1,2,3,5,6,9,10,15,18,30,45,90
Factors of 85
List of positive integer factors of 85 that divides 85 without a remainder.
1,5,17,85
Factors of 59
List of positive integer factors of 59 that divides 59 without a remainder.
1,59
Greatest Common Factor
We found the factors 81,90,85,59 . The biggest common factor number is the GCF number.
So the greatest common factor 81,90,85,59 is 1.
Lets's calculate LCM of 18,21,42,687
2 | 18, 21, 42, 687 |
3 | 9, 21, 21, 687 |
7 | 3, 7, 7, 229 |
3, 1, 1, 229 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 3 x 1 x 1 x 229 = 28854
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/28854
Therefore, the GCF of Fractions 81/18,90/21,85/42,59/687 is 1/28854
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 18,21,42,687 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,21,42,687) = 3
common factors(in case of two or more numbers have common factors) = 126
GCF(18,21,42,687) x common factors =3 x 126 = 378
LCM(18,21,42,687) = ( 18 × 21 × 42 × 687 ) / 378
LCM(18,21,42,687) = 10906812 / 378
LCM(18,21,42,687) = 28854
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 81/18, 90/21, 85/42, 59/687?
Answer: GCF of Numerators as per given numbers 81/18, 90/21, 85/42, 59/687 is
GCF of Numerators i.e. for 81,90,85,59 is 1
LCM of denominators i.e. for 18,21,42,687 is 28854.
Thus, GCF of Fractions is 1/28854.Finally, GCF of Fractions for 81/18, 90/21, 85/42, 59/687 is 1/28854.