Use our free GCF of Fractions Calculator tool to compute the GCF of 872/678, 184/510 i.e 8/57630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 872/678, 184/510.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 872/678,184/510
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 872/678,184/510, numerators are 872,184
Denominators are 678,510
The GCF of 872,184 is 8 .
LCM of 678,510 is 57630.
The greatest common factor of 872/678,184/510 = [GCF of 872,184]/[LCM of 678,510]= 8/57630
Therefore, the GCF of 872/678,184/510 is 8/57630.
To find the highest common factor of 872,184, we have to find the factors of both numbers and list the highest common factor.
The factors of 872 are 1, 2, 4, 8, 109, 218, 436, 872
The factors of 184 are 1, 2, 4, 8, 23, 46, 92, 184
The HCF of 872,184 is 8.
Lets's calculate GCF of 872,184
2 | 872, 184 |
2 | 436, 92 |
2 | 218, 46 |
109, 23 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 872
:1,2,4,8,109,218,436,872
Now, list down the factors of 184
:1,2,4,8,23,46,92,184
Greatest Common Factor
We found the factors 872,184 . The biggest common factor number is the GCF number.
So the greatest common factor 872,184 is 8.
Lets's calculate LCM of 678,510
2 | 678, 510 |
3 | 339, 255 |
113, 85 |
∴ So the LCM of the given numbers is 2 x 3 x 113 x 85 = 57630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/57630
Therefore, the GCF of Fractions 872/678,184/510 is 8/57630
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 678,510 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,510) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(678,510) x common factors =6 x 1 = 6
LCM(678,510) = ( 678 × 510 ) / 6
LCM(678,510) = 345780 / 6
LCM(678,510) = 57630
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 872,184?
The HCF of 872,184 is 8
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 872/678, 184/510?
Answer: GCF of Numerators as per given numbers 872/678, 184/510 is
GCF of Numerators i.e. for 872,184 is 8
LCM of denominators i.e. for 678,510 is 57630.
Thus, GCF of Fractions is 8/57630.Finally, GCF of Fractions for 872/678, 184/510 is 8/57630.