Use our free GCF of Fractions Calculator tool to compute the GCF of 80/421, 76/579, 120/810 i.e 4/65814930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 80/421, 76/579, 120/810.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 80/421,76/579,120/810
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 80/421,76/579,120/810, numerators are 80,76,120
Denominators are 421,579,810
The GCF of 80,76,120 is 4 .
LCM of 421,579,810 is 65814930.
The greatest common factor of 80/421,76/579,120/810 = [GCF of 80,76,120]/[LCM of 421,579,810]= 4/65814930
Therefore, the GCF of 80/421,76/579,120/810 is 4/65814930.
To find the highest common factor of 80,76,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 76 are 1, 2, 4, 19, 38, 76
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 80,76,120 is 4.
Lets's calculate GCF of 80,76,120
2 | 80, 76, 120 |
2 | 40, 38, 60 |
20, 19, 30 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 76
:1,2,4,19,38,76
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 80,76,120 . The biggest common factor number is the GCF number.
So the greatest common factor 80,76,120 is 4.
Lets's calculate LCM of 421,579,810
3 | 421, 579, 810 |
421, 193, 270 |
∴ So the LCM of the given numbers is 3 x 421 x 193 x 270 = 65814930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/65814930
Therefore, the GCF of Fractions 80/421,76/579,120/810 is 4/65814930
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 421,579,810 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(421,579,810) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(421,579,810) x common factors =1 x 3 = 3
LCM(421,579,810) = ( 421 × 579 × 810 ) / 3
LCM(421,579,810) = 197444790 / 3
LCM(421,579,810) = 65814930
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 80,76,120?
The HCF of 80,76,120 is 4
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 80/421, 76/579, 120/810?
Answer: GCF of Numerators as per given numbers 80/421, 76/579, 120/810 is
GCF of Numerators i.e. for 80,76,120 is 4
LCM of denominators i.e. for 421,579,810 is 65814930.
Thus, GCF of Fractions is 4/65814930.Finally, GCF of Fractions for 80/421, 76/579, 120/810 is 4/65814930.