Use our free GCF of Fractions Calculator tool to compute the GCF of 428/651, 580/868 i.e 4/2604 easily. The following is the detailed procedure to determine the greatest common factor of fractions 428/651, 580/868.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 428/651,580/868
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 428/651,580/868, numerators are 428,580
Denominators are 651,868
The GCF of 428,580 is 4 .
LCM of 651,868 is 2604.
The greatest common factor of 428/651,580/868 = [GCF of 428,580]/[LCM of 651,868]= 4/2604
Therefore, the GCF of 428/651,580/868 is 4/2604.
To find the highest common factor of 428,580, we have to find the factors of both numbers and list the highest common factor.
The factors of 428 are 1, 2, 4, 107, 214, 428
The factors of 580 are 1, 2, 4, 5, 10, 20, 29, 58, 116, 145, 290, 580
The HCF of 428,580 is 4.
Lets's calculate GCF of 428,580
2 | 428, 580 |
2 | 214, 290 |
107, 145 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 428
:1,2,4,107,214,428
Now, list down the factors of 580
:1,2,4,5,10,20,29,58,116,145,290,580
Greatest Common Factor
We found the factors 428,580 . The biggest common factor number is the GCF number.
So the greatest common factor 428,580 is 4.
Lets's calculate LCM of 651,868
7 | 651, 868 |
31 | 93, 124 |
3, 4 |
∴ So the LCM of the given numbers is 7 x 31 x 3 x 4 = 2604
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/2604
Therefore, the GCF of Fractions 428/651,580/868 is 4/2604
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 651,868 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(651,868) = 217
common factors(in case of two or more numbers have common factors) = 1
GCF(651,868) x common factors =217 x 1 = 217
LCM(651,868) = ( 651 × 868 ) / 217
LCM(651,868) = 565068 / 217
LCM(651,868) = 2604
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 428,580?
The HCF of 428,580 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 428/651, 580/868?
Answer: GCF of Numerators as per given numbers 428/651, 580/868 is
GCF of Numerators i.e. for 428,580 is 4
LCM of denominators i.e. for 651,868 is 2604.
Thus, GCF of Fractions is 4/2604.Finally, GCF of Fractions for 428/651, 580/868 is 4/2604.