Use our free GCF of Fractions Calculator tool to compute the GCF of 206/581, 278/125 i.e 2/72625 easily. The following is the detailed procedure to determine the greatest common factor of fractions 206/581, 278/125.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 206/581,278/125
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 206/581,278/125, numerators are 206,278
Denominators are 581,125
The GCF of 206,278 is 2 .
LCM of 581,125 is 72625.
The greatest common factor of 206/581,278/125 = [GCF of 206,278]/[LCM of 581,125]= 2/72625
Therefore, the GCF of 206/581,278/125 is 2/72625.
To find the highest common factor of 206,278, we have to find the factors of both numbers and list the highest common factor.
The factors of 206 are 1, 2, 103, 206
The factors of 278 are 1, 2, 139, 278
The HCF of 206,278 is 2.
Lets's calculate GCF of 206,278
2 | 206, 278 |
103, 139 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 206
:1,2,103,206
Now, list down the factors of 278
:1,2,139,278
Greatest Common Factor
We found the factors 206,278 . The biggest common factor number is the GCF number.
So the greatest common factor 206,278 is 2.
Lets's calculate LCM of 581,125
Given numbers has no common factors except 1. So, there LCM is their product i.e 72625
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/72625
Therefore, the GCF of Fractions 206/581,278/125 is 2/72625
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 581,125 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(581,125) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(581,125) x common factors =1 x 1 = 1
LCM(581,125) = ( 581 × 125 ) / 1
LCM(581,125) = 72625 / 1
LCM(581,125) = 72625
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 206,278?
The HCF of 206,278 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 206/581, 278/125?
Answer: GCF of Numerators as per given numbers 206/581, 278/125 is
GCF of Numerators i.e. for 206,278 is 2
LCM of denominators i.e. for 581,125 is 72625.
Thus, GCF of Fractions is 2/72625.Finally, GCF of Fractions for 206/581, 278/125 is 2/72625.