Use our free GCF of Fractions Calculator tool to compute the GCF of 168/856, 7630/578 i.e 14/247384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/856, 7630/578.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 168/856,7630/578
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 168/856,7630/578, numerators are 168,7630
Denominators are 856,578
The GCF of 168,7630 is 14 .
LCM of 856,578 is 247384.
The greatest common factor of 168/856,7630/578 = [GCF of 168,7630]/[LCM of 856,578]= 14/247384
Therefore, the GCF of 168/856,7630/578 is 14/247384.
To find the highest common factor of 168,7630, we have to find the factors of both numbers and list the highest common factor.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 7630 are 1, 2, 5, 7, 10, 14, 35, 70, 109, 218, 545, 763, 1090, 1526, 3815, 7630
The HCF of 168,7630 is 14.
Lets's calculate GCF of 168,7630
2 | 168, 7630 |
7 | 84, 3815 |
12, 545 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Now, list down the factors of 7630
:1,2,5,7,10,14,35,70,109,218,545,763,1090,1526,3815,7630
Greatest Common Factor
We found the factors 168,7630 . The biggest common factor number is the GCF number.
So the greatest common factor 168,7630 is 14.
Lets's calculate LCM of 856,578
2 | 856, 578 |
428, 289 |
∴ So the LCM of the given numbers is 2 x 428 x 289 = 247384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/247384
Therefore, the GCF of Fractions 168/856,7630/578 is 14/247384
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 856,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(856,578) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(856,578) x common factors =2 x 1 = 2
LCM(856,578) = ( 856 × 578 ) / 2
LCM(856,578) = 494768 / 2
LCM(856,578) = 247384
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 168,7630?
The HCF of 168,7630 is 14
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 168/856, 7630/578?
Answer: GCF of Numerators as per given numbers 168/856, 7630/578 is
GCF of Numerators i.e. for 168,7630 is 14
LCM of denominators i.e. for 856,578 is 247384.
Thus, GCF of Fractions is 14/247384.Finally, GCF of Fractions for 168/856, 7630/578 is 14/247384.