Use our free GCF of Fractions Calculator tool to compute the GCF of 82/871, 46/173, 840/221 i.e 2/2561611 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/871, 46/173, 840/221.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 82/871,46/173,840/221
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 82/871,46/173,840/221, numerators are 82,46,840
Denominators are 871,173,221
The GCF of 82,46,840 is 2 .
LCM of 871,173,221 is 2561611.
The greatest common factor of 82/871,46/173,840/221 = [GCF of 82,46,840]/[LCM of 871,173,221]= 2/2561611
Therefore, the GCF of 82/871,46/173,840/221 is 2/2561611.
To find the highest common factor of 82,46,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 46 are 1, 2, 23, 46
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 82,46,840 is 2.
Lets's calculate GCF of 82,46,840
2 | 82, 46, 840 |
41, 23, 420 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 46
:1,2,23,46
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 82,46,840 . The biggest common factor number is the GCF number.
So the greatest common factor 82,46,840 is 2.
Lets's calculate LCM of 871,173,221
13 | 871, 173, 221 |
67, 173, 17 |
∴ So the LCM of the given numbers is 13 x 67 x 173 x 17 = 2561611
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2561611
Therefore, the GCF of Fractions 82/871,46/173,840/221 is 2/2561611
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 871,173,221 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(871,173,221) = 1
common factors(in case of two or more numbers have common factors) = 13
GCF(871,173,221) x common factors =1 x 13 = 13
LCM(871,173,221) = ( 871 × 173 × 221 ) / 13
LCM(871,173,221) = 33300943 / 13
LCM(871,173,221) = 2561611
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 82,46,840?
The HCF of 82,46,840 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 82/871, 46/173, 840/221?
Answer: GCF of Numerators as per given numbers 82/871, 46/173, 840/221 is
GCF of Numerators i.e. for 82,46,840 is 2
LCM of denominators i.e. for 871,173,221 is 2561611.
Thus, GCF of Fractions is 2/2561611.Finally, GCF of Fractions for 82/871, 46/173, 840/221 is 2/2561611.