Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 48/21,68/81,61/99,69/22
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 48,68,61,69
Greatest Common Factor of Numerators i.e. GCF of 48,68,61,69 is 1 .
LCM of Denominators means LCM of 21,81,99,22 as per the given fractions.
LCM of 21,81,99,22 is 12474 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 48,68,61,69
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 48
List of positive integer factors of 48 that divides 48 without a remainder.
1,2,3,4,6,8,12,16,24,48
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 61
List of positive integer factors of 61 that divides 61 without a remainder.
1,61
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
Greatest Common Factor
We found the factors 48,68,61,69 . The biggest common factor number is the GCF number.
So the greatest common factor 48,68,61,69 is 1.
Lets's calculate LCM of 21,81,99,22
3 | 21, 81, 99, 22 |
3 | 7, 27, 33, 22 |
11 | 7, 9, 11, 22 |
7, 9, 1, 2 |
∴ So the LCM of the given numbers is 3 x 3 x 11 x 7 x 9 x 1 x 2 = 12474
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12474
Therefore, the GCF of Fractions 48/21,68/81,61/99,69/22 is 1/12474
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 21,81,99,22 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,81,99,22) = 1
common factors(in case of two or more numbers have common factors) = 297
GCF(21,81,99,22) x common factors =1 x 297 = 297
LCM(21,81,99,22) = ( 21 × 81 × 99 × 22 ) / 297
LCM(21,81,99,22) = 3704778 / 297
LCM(21,81,99,22) = 12474
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 48/21, 68/81, 61/99, 69/22?
Answer: GCF of Numerators as per given numbers 48/21, 68/81, 61/99, 69/22 is
GCF of Numerators i.e. for 48,68,61,69 is 1
LCM of denominators i.e. for 21,81,99,22 is 12474.
Thus, GCF of Fractions is 1/12474.Finally, GCF of Fractions for 48/21, 68/81, 61/99, 69/22 is 1/12474.