Use our free GCF of Fractions Calculator tool to compute the GCF of 580/197, 214/901 i.e 2/177497 easily. The following is the detailed procedure to determine the greatest common factor of fractions 580/197, 214/901.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 580/197,214/901
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 580/197,214/901, numerators are 580,214
Denominators are 197,901
The GCF of 580,214 is 2 .
LCM of 197,901 is 177497.
The greatest common factor of 580/197,214/901 = [GCF of 580,214]/[LCM of 197,901]= 2/177497
Therefore, the GCF of 580/197,214/901 is 2/177497.
To find the highest common factor of 580,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The factors of 214 are 1, 2, 107, 214
The HCF of 580,214 is 2.
Lets's calculate GCF of 580,214
2 | 580, 214 |
290, 107 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 580,214 . The biggest common factor number is the GCF number.
So the greatest common factor 580,214 is 2.
Lets's calculate LCM of 197,901
Given numbers has no common factors except 1. So, there LCM is their product i.e 177497
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/177497
Therefore, the GCF of Fractions 580/197,214/901 is 2/177497
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 197,901 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(197,901) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(197,901) x common factors =1 x 1 = 1
LCM(197,901) = ( 197 × 901 ) / 1
LCM(197,901) = 177497 / 1
LCM(197,901) = 177497
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 580,214?
The HCF of 580,214 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 580/197, 214/901?
Answer: GCF of Numerators as per given numbers 580/197, 214/901 is
GCF of Numerators i.e. for 580,214 is 2
LCM of denominators i.e. for 197,901 is 177497.
Thus, GCF of Fractions is 2/177497.Finally, GCF of Fractions for 580/197, 214/901 is 2/177497.