Use our free GCF of Fractions Calculator tool to compute the GCF of 285/560, 7776/8222 i.e 3/2302160 easily. The following is the detailed procedure to determine the greatest common factor of fractions 285/560, 7776/8222.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 285/560,7776/8222
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 285/560,7776/8222, numerators are 285,7776
Denominators are 560,8222
The GCF of 285,7776 is 3 .
LCM of 560,8222 is 2302160.
The greatest common factor of 285/560,7776/8222 = [GCF of 285,7776]/[LCM of 560,8222]= 3/2302160
Therefore, the GCF of 285/560,7776/8222 is 3/2302160.
To find the highest common factor of 285,7776, we have to find the factors of both numbers and list the highest common factor.
The factors of 285 are 1, 3, 5, 15, 19, 57, 95, 285
The factors of 7776 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 81, 96, 108, 144, 162, 216, 243, 288, 324, 432, 486, 648, 864, 972, 1296, 1944, 2592, 3888, 7776
The HCF of 285,7776 is 3.
Lets's calculate GCF of 285,7776
3 | 285, 7776 |
95, 2592 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 285
:1,3,5,15,19,57,95,285
Now, list down the factors of 7776
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,81,96,108,144,162,216,243,288,324,432,486,648,864,972,1296,1944,2592,3888,7776
Greatest Common Factor
We found the factors 285,7776 . The biggest common factor number is the GCF number.
So the greatest common factor 285,7776 is 3.
Lets's calculate LCM of 560,8222
2 | 560, 8222 |
280, 4111 |
∴ So the LCM of the given numbers is 2 x 280 x 4111 = 2302160
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2302160
Therefore, the GCF of Fractions 285/560,7776/8222 is 3/2302160
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 560,8222 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(560,8222) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(560,8222) x common factors =2 x 1 = 2
LCM(560,8222) = ( 560 × 8222 ) / 2
LCM(560,8222) = 4604320 / 2
LCM(560,8222) = 2302160
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 285,7776?
The HCF of 285,7776 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 285/560, 7776/8222?
Answer: GCF of Numerators as per given numbers 285/560, 7776/8222 is
GCF of Numerators i.e. for 285,7776 is 3
LCM of denominators i.e. for 560,8222 is 2302160.
Thus, GCF of Fractions is 3/2302160.Finally, GCF of Fractions for 285/560, 7776/8222 is 3/2302160.