Use our free GCF of Fractions Calculator tool to compute the GCF of 770/398, 172/866 i.e 2/172334 easily. The following is the detailed procedure to determine the greatest common factor of fractions 770/398, 172/866.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 770/398,172/866
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 770/398,172/866, numerators are 770,172
Denominators are 398,866
The GCF of 770,172 is 2 .
LCM of 398,866 is 172334.
The greatest common factor of 770/398,172/866 = [GCF of 770,172]/[LCM of 398,866]= 2/172334
Therefore, the GCF of 770/398,172/866 is 2/172334.
To find the highest common factor of 770,172, we have to find the factors of both numbers and list the highest common factor.
The factors of 770 are 1, 2, 5, 7, 10, 11, 14, 22, 35, 55, 70, 77, 110, 154, 385, 770
The factors of 172 are 1, 2, 4, 43, 86, 172
The HCF of 770,172 is 2.
Lets's calculate GCF of 770,172
2 | 770, 172 |
385, 86 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 770
:1,2,5,7,10,11,14,22,35,55,70,77,110,154,385,770
Now, list down the factors of 172
:1,2,4,43,86,172
Greatest Common Factor
We found the factors 770,172 . The biggest common factor number is the GCF number.
So the greatest common factor 770,172 is 2.
Lets's calculate LCM of 398,866
2 | 398, 866 |
199, 433 |
∴ So the LCM of the given numbers is 2 x 199 x 433 = 172334
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/172334
Therefore, the GCF of Fractions 770/398,172/866 is 2/172334
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 398,866 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(398,866) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(398,866) x common factors =2 x 1 = 2
LCM(398,866) = ( 398 × 866 ) / 2
LCM(398,866) = 344668 / 2
LCM(398,866) = 172334
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 770,172?
The HCF of 770,172 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 770/398, 172/866?
Answer: GCF of Numerators as per given numbers 770/398, 172/866 is
GCF of Numerators i.e. for 770,172 is 2
LCM of denominators i.e. for 398,866 is 172334.
Thus, GCF of Fractions is 2/172334.Finally, GCF of Fractions for 770/398, 172/866 is 2/172334.