Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 17/205,140/225
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 17,140
Greatest Common Factor of Numerators i.e. GCF of 17,140 is 1 .
LCM of Denominators means LCM of 205,225 as per the given fractions.
LCM of 205,225 is 9225 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 17,140
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 17
List of positive integer factors of 17 that divides 17 without a remainder.
1,17
Factors of 140
List of positive integer factors of 140 that divides 140 without a remainder.
1,2,4,5,7,10,14,20,28,35,70,140
Greatest Common Factor
We found the factors 17,140 . The biggest common factor number is the GCF number.
So the greatest common factor 17,140 is 1.
Lets's calculate LCM of 205,225
5 | 205, 225 |
41, 45 |
∴ So the LCM of the given numbers is 5 x 41 x 45 = 9225
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9225
Therefore, the GCF of Fractions 17/205,140/225 is 1/9225
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 205,225 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,225) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(205,225) x common factors =5 x 1 = 5
LCM(205,225) = ( 205 × 225 ) / 5
LCM(205,225) = 46125 / 5
LCM(205,225) = 9225
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 17/205, 140/225?
Answer: GCF of Numerators as per given numbers 17/205, 140/225 is
GCF of Numerators i.e. for 17,140 is 1
LCM of denominators i.e. for 205,225 is 9225.
Thus, GCF of Fractions is 1/9225.Finally, GCF of Fractions for 17/205, 140/225 is 1/9225.