Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 197/512,609/416
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 197,609
Greatest Common Factor of Numerators i.e. GCF of 197,609 is 1 .
LCM of Denominators means LCM of 512,416 as per the given fractions.
LCM of 512,416 is 6656 as it is the smallest common factor for both these numbers.
Lets's calculate GCF of 197,609
∴ So GCF of numbers is 1 because of no common factors present between them.
Factors of 197
List of positive integer factors of 197 that divides 197 without a remainder.
1,197
Factors of 609
List of positive integer factors of 609 that divides 609 without a remainder.
1,3,7,21,29,87,203,609
Greatest Common Factor
We found the factors 197,609 . The biggest common factor number is the GCF number.
So the greatest common factor 197,609 is 1.
Lets's calculate LCM of 512,416
2 | 512, 416 |
2 | 256, 208 |
2 | 128, 104 |
2 | 64, 52 |
2 | 32, 26 |
16, 13 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 16 x 13 = 6656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6656
Therefore, the GCF of Fractions 197/512,609/416 is 1/6656
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 512,416 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,416) = 32
common factors(in case of two or more numbers have common factors) = 1
GCF(512,416) x common factors =32 x 1 = 32
LCM(512,416) = ( 512 × 416 ) / 32
LCM(512,416) = 212992 / 32
LCM(512,416) = 6656
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 197/512, 609/416?
Answer: GCF of Numerators as per given numbers 197/512, 609/416 is
GCF of Numerators i.e. for 197,609 is 1
LCM of denominators i.e. for 512,416 is 6656.
Thus, GCF of Fractions is 1/6656.Finally, GCF of Fractions for 197/512, 609/416 is 1/6656.