Use our free GCF of Fractions Calculator tool to compute the GCF of 873/112, 414/892 i.e 9/24976 easily. The following is the detailed procedure to determine the greatest common factor of fractions 873/112, 414/892.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 873/112,414/892
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 873/112,414/892, numerators are 873,414
Denominators are 112,892
The GCF of 873,414 is 9 .
LCM of 112,892 is 24976.
The greatest common factor of 873/112,414/892 = [GCF of 873,414]/[LCM of 112,892]= 9/24976
Therefore, the GCF of 873/112,414/892 is 9/24976.
To find the highest common factor of 873,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 873 are 1, 3, 9, 97, 291, 873
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 873,414 is 9.
Lets's calculate GCF of 873,414
3 | 873, 414 |
3 | 291, 138 |
97, 46 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Now, list down the factors of 873
:1,3,9,97,291,873
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 873,414 . The biggest common factor number is the GCF number.
So the greatest common factor 873,414 is 9.
Lets's calculate LCM of 112,892
2 | 112, 892 |
2 | 56, 446 |
28, 223 |
∴ So the LCM of the given numbers is 2 x 2 x 28 x 223 = 24976
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/24976
Therefore, the GCF of Fractions 873/112,414/892 is 9/24976
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 112,892 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(112,892) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(112,892) x common factors =4 x 1 = 4
LCM(112,892) = ( 112 × 892 ) / 4
LCM(112,892) = 99904 / 4
LCM(112,892) = 24976
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 873,414?
The HCF of 873,414 is 9
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 873/112, 414/892?
Answer: GCF of Numerators as per given numbers 873/112, 414/892 is
GCF of Numerators i.e. for 873,414 is 9
LCM of denominators i.e. for 112,892 is 24976.
Thus, GCF of Fractions is 9/24976.Finally, GCF of Fractions for 873/112, 414/892 is 9/24976.