Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 23/78,97/40,17/31,69/625
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 23,97,17,69
Greatest Common Factor of Numerators i.e. GCF of 23,97,17,69 is 1 .
LCM of Denominators means LCM of 78,40,31,625 as per the given fractions.
LCM of 78,40,31,625 is 6045000 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 23,97,17,69
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 23
List of positive integer factors of 23 that divides 23 without a remainder.
1,23
Factors of 97
List of positive integer factors of 97 that divides 97 without a remainder.
1,97
Factors of 17
List of positive integer factors of 17 that divides 17 without a remainder.
1,17
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 23,97,17,69 . The biggest common factor number is the GCF number.
So the greatest common factor 23,97,17,69 is 1.
Lets's calculate LCM of 78,40,31,625
2 | 78, 40, 31, 625 |
5 | 39, 20, 31, 625 |
39, 4, 31, 125 |
∴ So the LCM of the given numbers is 2 x 5 x 39 x 4 x 31 x 125 = 6045000
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6045000
Therefore, the GCF of Fractions 23/78,97/40,17/31,69/625 is 1/6045000
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 78,40,31,625 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,40,31,625) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(78,40,31,625) x common factors =1 x 10 = 10
LCM(78,40,31,625) = ( 78 × 40 × 31 × 625 ) / 10
LCM(78,40,31,625) = 60450000 / 10
LCM(78,40,31,625) = 6045000
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 23/78, 97/40, 17/31, 69/625?
Answer: GCF of Numerators as per given numbers 23/78, 97/40, 17/31, 69/625 is
GCF of Numerators i.e. for 23,97,17,69 is 1
LCM of denominators i.e. for 78,40,31,625 is 6045000.
Thus, GCF of Fractions is 1/6045000.Finally, GCF of Fractions for 23/78, 97/40, 17/31, 69/625 is 1/6045000.