Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 99/12,43/30,74/23,807/40
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 99,43,74,807
Greatest Common Factor of Numerators i.e. GCF of 99,43,74,807 is 1 .
LCM of Denominators means LCM of 12,30,23,40 as per the given fractions.
LCM of 12,30,23,40 is 2760 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 99,43,74,807
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 99
List of positive integer factors of 99 that divides 99 without a remainder.
1,3,9,11,33,99
Factors of 43
List of positive integer factors of 43 that divides 43 without a remainder.
1,43
Factors of 74
List of positive integer factors of 74 that divides 74 without a remainder.
1,2,37,74
Factors of 807
List of positive integer factors of 807 that divides 807 without a remainder.
1,3,269,807
Greatest Common Factor
We found the factors 99,43,74,807 . The biggest common factor number is the GCF number.
So the greatest common factor 99,43,74,807 is 1.
Lets's calculate LCM of 12,30,23,40
2 | 12, 30, 23, 40 |
2 | 6, 15, 23, 20 |
3 | 3, 15, 23, 10 |
5 | 1, 5, 23, 10 |
1, 1, 23, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 1 x 1 x 23 x 2 = 2760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2760
Therefore, the GCF of Fractions 99/12,43/30,74/23,807/40 is 1/2760
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 12,30,23,40 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,30,23,40) = 1
common factors(in case of two or more numbers have common factors) = 120
GCF(12,30,23,40) x common factors =1 x 120 = 120
LCM(12,30,23,40) = ( 12 × 30 × 23 × 40 ) / 120
LCM(12,30,23,40) = 331200 / 120
LCM(12,30,23,40) = 2760
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 99/12, 43/30, 74/23, 807/40?
Answer: GCF of Numerators as per given numbers 99/12, 43/30, 74/23, 807/40 is
GCF of Numerators i.e. for 99,43,74,807 is 1
LCM of denominators i.e. for 12,30,23,40 is 2760.
Thus, GCF of Fractions is 1/2760.Finally, GCF of Fractions for 99/12, 43/30, 74/23, 807/40 is 1/2760.