Use our free GCF of Fractions Calculator tool to compute the GCF of 398/972, 680/209 i.e 2/203148 easily. The following is the detailed procedure to determine the greatest common factor of fractions 398/972, 680/209.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 398/972,680/209
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 398/972,680/209, numerators are 398,680
Denominators are 972,209
The GCF of 398,680 is 2 .
LCM of 972,209 is 203148.
The greatest common factor of 398/972,680/209 = [GCF of 398,680]/[LCM of 972,209]= 2/203148
Therefore, the GCF of 398/972,680/209 is 2/203148.
To find the highest common factor of 398,680, we have to find the factors of both numbers and list the highest common factor.
The factors of 398 are 1, 2, 199, 398
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The HCF of 398,680 is 2.
Lets's calculate GCF of 398,680
2 | 398, 680 |
199, 340 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 398
:1,2,199,398
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Greatest Common Factor
We found the factors 398,680 . The biggest common factor number is the GCF number.
So the greatest common factor 398,680 is 2.
Lets's calculate LCM of 972,209
Given numbers has no common factors except 1. So, there LCM is their product i.e 203148
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/203148
Therefore, the GCF of Fractions 398/972,680/209 is 2/203148
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 972,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(972,209) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(972,209) x common factors =1 x 1 = 1
LCM(972,209) = ( 972 × 209 ) / 1
LCM(972,209) = 203148 / 1
LCM(972,209) = 203148
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 398,680?
The HCF of 398,680 is 2
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. 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.
4. What is the GCF of Fractions for 398/972, 680/209?
Answer: GCF of Numerators as per given numbers 398/972, 680/209 is
GCF of Numerators i.e. for 398,680 is 2
LCM of denominators i.e. for 972,209 is 203148.
Thus, GCF of Fractions is 2/203148.Finally, GCF of Fractions for 398/972, 680/209 is 2/203148.