Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 343/512,3059/698
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 343,3059
Greatest Common Factor of Numerators i.e. GCF of 343,3059 is 7 .
LCM of Denominators means LCM of 512,698 as per the given fractions.
LCM of 512,698 is 178688 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 343,3059
7 | 343, 3059 |
49, 437 |
∴ So the GCF of the given numbers is 7 = 7
Factors of 343
List of positive integer factors of 343 that divides 343 without a remainder.
1,7,49,343
Factors of 3059
List of positive integer factors of 3059 that divides 3059 without a remainder.
1,7,19,23,133,161,437,3059
Greatest Common Factor
We found the factors 343,3059 . The biggest common factor number is the GCF number.
So the greatest common factor 343,3059 is 7.
Lets's calculate LCM of 512,698
2 | 512, 698 |
256, 349 |
∴ So the LCM of the given numbers is 2 x 256 x 349 = 178688
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/178688
Therefore, the GCF of Fractions 343/512,3059/698 is 7/178688
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 512,698 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,698) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(512,698) x common factors =2 x 1 = 2
LCM(512,698) = ( 512 × 698 ) / 2
LCM(512,698) = 357376 / 2
LCM(512,698) = 178688
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 343/512, 3059/698?
Answer: GCF of Numerators as per given numbers 343/512, 3059/698 is
GCF of Numerators i.e. for 343,3059 is 7
LCM of denominators i.e. for 512,698 is 178688.
Thus, GCF of Fractions is 7/178688.Finally, GCF of Fractions for 343/512, 3059/698 is 7/178688.