Use our free GCF of Fractions Calculator tool to compute the GCF of 315/546, 8823/3122 i.e 3/121758 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/546, 8823/3122.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 315/546,8823/3122
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 315/546,8823/3122, numerators are 315,8823
Denominators are 546,3122
The GCF of 315,8823 is 3 .
LCM of 546,3122 is 121758.
The greatest common factor of 315/546,8823/3122 = [GCF of 315,8823]/[LCM of 546,3122]= 3/121758
Therefore, the GCF of 315/546,8823/3122 is 3/121758.
To find the highest common factor of 315,8823, we have to find the factors of both numbers and list the highest common factor.
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
The factors of 8823 are 1, 3, 17, 51, 173, 519, 2941, 8823
The HCF of 315,8823 is 3.
Lets's calculate GCF of 315,8823
3 | 315, 8823 |
105, 2941 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 315
:1,3,5,7,9,15,21,35,45,63,105,315
Now, list down the factors of 8823
:1,3,17,51,173,519,2941,8823
Greatest Common Factor
We found the factors 315,8823 . The biggest common factor number is the GCF number.
So the greatest common factor 315,8823 is 3.
Lets's calculate LCM of 546,3122
2 | 546, 3122 |
7 | 273, 1561 |
39, 223 |
∴ So the LCM of the given numbers is 2 x 7 x 39 x 223 = 121758
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/121758
Therefore, the GCF of Fractions 315/546,8823/3122 is 3/121758
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 546,3122 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,3122) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(546,3122) x common factors =14 x 1 = 14
LCM(546,3122) = ( 546 × 3122 ) / 14
LCM(546,3122) = 1704612 / 14
LCM(546,3122) = 121758
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 315,8823?
The HCF of 315,8823 is 3
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 315/546, 8823/3122?
Answer: GCF of Numerators as per given numbers 315/546, 8823/3122 is
GCF of Numerators i.e. for 315,8823 is 3
LCM of denominators i.e. for 546,3122 is 121758.
Thus, GCF of Fractions is 3/121758.Finally, GCF of Fractions for 315/546, 8823/3122 is 3/121758.