Get help with finding GCF of fractions 6/63, 21/81, 27/108, 105/120 using GCF of Fractions Calculator to know the result 3/22680 the largest number that divides all the numbers with a zero remainder.
Greatest common factor (GCF) of 6/63, 21/81, 27/108, 105/120 is 3/22680.
GCF(6/63, 21/81, 27/108, 105/120) = 3/22680
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 6/63,21/81,27/108,105/120
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 6,21,27,105
Greatest Common Factor of Numerators i.e. GCF of 6,21,27,105 is 3 .
LCM of Denominators means LCM of 63,81,108,120 as per the given fractions.
LCM of 63,81,108,120 is 22680 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 6,21,27,105
3 | 6, 21, 27, 105 |
2, 7, 9, 35 |
∴ So the GCF of the given numbers is 3 = 3
Factors of 6
List of positive integer factors of 6 that divides 6 without a remainder.
1,2,3,6
Factors of 21
List of positive integer factors of 21 that divides 21 without a remainder.
1,3,7,21
Factors of 27
List of positive integer factors of 27 that divides 27 without a remainder.
1,3,9,27
Factors of 105
List of positive integer factors of 105 that divides 105 without a remainder.
1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 6,21,27,105 . The biggest common factor number is the GCF number.
So the greatest common factor 6,21,27,105 is 3.
Lets's calculate LCM of 63,81,108,120
2 | 63, 81, 108, 120 |
2 | 63, 81, 54, 60 |
3 | 63, 81, 27, 30 |
3 | 21, 9, 27, 10 |
3 | 7, 3, 9, 10 |
7, 1, 3, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 3 x 3 x 7 x 1 x 3 x 10 = 22680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/22680
Therefore, the GCF of Fractions 6/63,21/81,27/108,105/120 is 3/22680
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 63,81,108,120 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(63,81,108,120) = 3
common factors(in case of two or more numbers have common factors) = 972
GCF(63,81,108,120) x common factors =3 x 972 = 2916
LCM(63,81,108,120) = ( 63 × 81 × 108 × 120 ) / 2916
LCM(63,81,108,120) = 66134880 / 2916
LCM(63,81,108,120) = 22680
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 6/63, 21/81, 27/108, 105/120?
Answer: GCF of Numerators as per given numbers 6/63, 21/81, 27/108, 105/120 is
GCF of Numerators i.e. for 6,21,27,105 is 3
LCM of denominators i.e. for 63,81,108,120 is 22680.
Thus, GCF of Fractions is 3/22680.Finally, GCF of Fractions for 6/63, 21/81, 27/108, 105/120 is 3/22680.