Use our free GCF of Fractions Calculator tool to compute the GCF of 868/572, 314/728 i.e 2/8008 easily. The following is the detailed procedure to determine the greatest common factor of fractions 868/572, 314/728.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 868/572,314/728
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 868/572,314/728, numerators are 868,314
Denominators are 572,728
The GCF of 868,314 is 2 .
LCM of 572,728 is 8008.
The greatest common factor of 868/572,314/728 = [GCF of 868,314]/[LCM of 572,728]= 2/8008
Therefore, the GCF of 868/572,314/728 is 2/8008.
To find the highest common factor of 868,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 868 are 1, 2, 4, 7, 14, 28, 31, 62, 124, 217, 434, 868
The factors of 314 are 1, 2, 157, 314
The HCF of 868,314 is 2.
Lets's calculate GCF of 868,314
2 | 868, 314 |
434, 157 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 868
:1,2,4,7,14,28,31,62,124,217,434,868
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 868,314 . The biggest common factor number is the GCF number.
So the greatest common factor 868,314 is 2.
Lets's calculate LCM of 572,728
2 | 572, 728 |
2 | 286, 364 |
13 | 143, 182 |
11, 14 |
∴ So the LCM of the given numbers is 2 x 2 x 13 x 11 x 14 = 8008
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8008
Therefore, the GCF of Fractions 868/572,314/728 is 2/8008
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 572,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(572,728) = 52
common factors(in case of two or more numbers have common factors) = 1
GCF(572,728) x common factors =52 x 1 = 52
LCM(572,728) = ( 572 × 728 ) / 52
LCM(572,728) = 416416 / 52
LCM(572,728) = 8008
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 868,314?
The HCF of 868,314 is 2
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 868/572, 314/728?
Answer: GCF of Numerators as per given numbers 868/572, 314/728 is
GCF of Numerators i.e. for 868,314 is 2
LCM of denominators i.e. for 572,728 is 8008.
Thus, GCF of Fractions is 2/8008.Finally, GCF of Fractions for 868/572, 314/728 is 2/8008.