Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 29/83,49/83,90/25,414/70
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 29,49,90,414
Greatest Common Factor of Numerators i.e. GCF of 29,49,90,414 is 1 .
LCM of Denominators means LCM of 83,83,25,70 as per the given fractions.
LCM of 83,83,25,70 is 29050 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 29,49,90,414
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 29
List of positive integer factors of 29 that divides 29 without a remainder.
1,29
Factors of 49
List of positive integer factors of 49 that divides 49 without a remainder.
1,7,49
Factors of 90
List of positive integer factors of 90 that divides 90 without a remainder.
1,2,3,5,6,9,10,15,18,30,45,90
Factors of 414
List of positive integer factors of 414 that divides 414 without a remainder.
1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 29,49,90,414 . The biggest common factor number is the GCF number.
So the greatest common factor 29,49,90,414 is 1.
Lets's calculate LCM of 83,83,25,70
5 | 83, 83, 25, 70 |
83 | 83, 83, 5, 14 |
1, 1, 5, 14 |
∴ So the LCM of the given numbers is 5 x 83 x 1 x 1 x 5 x 14 = 29050
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/29050
Therefore, the GCF of Fractions 29/83,49/83,90/25,414/70 is 1/29050
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 83,83,25,70 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(83,83,25,70) = 1
common factors(in case of two or more numbers have common factors) = 415
GCF(83,83,25,70) x common factors =1 x 415 = 415
LCM(83,83,25,70) = ( 83 × 83 × 25 × 70 ) / 415
LCM(83,83,25,70) = 12055750 / 415
LCM(83,83,25,70) = 29050
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 29/83, 49/83, 90/25, 414/70?
Answer: GCF of Numerators as per given numbers 29/83, 49/83, 90/25, 414/70 is
GCF of Numerators i.e. for 29,49,90,414 is 1
LCM of denominators i.e. for 83,83,25,70 is 29050.
Thus, GCF of Fractions is 1/29050.Finally, GCF of Fractions for 29/83, 49/83, 90/25, 414/70 is 1/29050.