Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 68/75,72/67,96/55,12/99
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 68,72,96,12
Greatest Common Factor of Numerators i.e. GCF of 68,72,96,12 is 4 .
LCM of Denominators means LCM of 75,67,55,99 as per the given fractions.
LCM of 75,67,55,99 is 165825 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 68,72,96,12
2 | 68, 72, 96, 12 |
2 | 34, 36, 48, 6 |
17, 18, 24, 3 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Factors of 68
List of positive integer factors of 68 that divides 68 without a remainder.
1,2,4,17,34,68
Factors of 72
List of positive integer factors of 72 that divides 72 without a remainder.
1,2,3,4,6,8,9,12,18,24,36,72
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 12
List of positive integer factors of 12 that divides 12 without a remainder.
1,2,3,4,6,12
Greatest Common Factor
We found the factors 68,72,96,12 . The biggest common factor number is the GCF number.
So the greatest common factor 68,72,96,12 is 4.
Lets's calculate LCM of 75,67,55,99
3 | 75, 67, 55, 99 |
5 | 25, 67, 55, 33 |
11 | 5, 67, 11, 33 |
5, 67, 1, 3 |
∴ So the LCM of the given numbers is 3 x 5 x 11 x 5 x 67 x 1 x 3 = 165825
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/165825
Therefore, the GCF of Fractions 68/75,72/67,96/55,12/99 is 4/165825
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 75,67,55,99 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,67,55,99) = 1
common factors(in case of two or more numbers have common factors) = 165
GCF(75,67,55,99) x common factors =1 x 165 = 165
LCM(75,67,55,99) = ( 75 × 67 × 55 × 99 ) / 165
LCM(75,67,55,99) = 27361125 / 165
LCM(75,67,55,99) = 165825
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 68/75, 72/67, 96/55, 12/99?
Answer: GCF of Numerators as per given numbers 68/75, 72/67, 96/55, 12/99 is
GCF of Numerators i.e. for 68,72,96,12 is 4
LCM of denominators i.e. for 75,67,55,99 is 165825.
Thus, GCF of Fractions is 4/165825.Finally, GCF of Fractions for 68/75, 72/67, 96/55, 12/99 is 4/165825.