Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 25/26,40/29,69/87,72/612
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 25,40,69,72
Greatest Common Factor of Numerators i.e. GCF of 25,40,69,72 is 1 .
LCM of Denominators means LCM of 26,29,87,612 as per the given fractions.
LCM of 26,29,87,612 is 230724 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 25,40,69,72
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 25
List of positive integer factors of 25 that divides 25 without a remainder.
1,5,25
Factors of 40
List of positive integer factors of 40 that divides 40 without a remainder.
1,2,4,5,8,10,20,40
Factors of 69
List of positive integer factors of 69 that divides 69 without a remainder.
1,3,23,69
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
Greatest Common Factor
We found the factors 25,40,69,72 . The biggest common factor number is the GCF number.
So the greatest common factor 25,40,69,72 is 1.
Lets's calculate LCM of 26,29,87,612
2 | 26, 29, 87, 612 |
3 | 13, 29, 87, 306 |
29 | 13, 29, 29, 102 |
13, 1, 1, 102 |
∴ So the LCM of the given numbers is 2 x 3 x 29 x 13 x 1 x 1 x 102 = 230724
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/230724
Therefore, the GCF of Fractions 25/26,40/29,69/87,72/612 is 1/230724
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 26,29,87,612 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(26,29,87,612) = 1
common factors(in case of two or more numbers have common factors) = 174
GCF(26,29,87,612) x common factors =1 x 174 = 174
LCM(26,29,87,612) = ( 26 × 29 × 87 × 612 ) / 174
LCM(26,29,87,612) = 40145976 / 174
LCM(26,29,87,612) = 230724
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 25/26, 40/29, 69/87, 72/612?
Answer: GCF of Numerators as per given numbers 25/26, 40/29, 69/87, 72/612 is
GCF of Numerators i.e. for 25,40,69,72 is 1
LCM of denominators i.e. for 26,29,87,612 is 230724.
Thus, GCF of Fractions is 1/230724.Finally, GCF of Fractions for 25/26, 40/29, 69/87, 72/612 is 1/230724.