Use our free GCF of Fractions Calculator tool to compute the GCF of 5416/788, 8712/2756 i.e 8/542932 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5416/788, 8712/2756.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 5416/788,8712/2756
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 5416/788,8712/2756, numerators are 5416,8712
Denominators are 788,2756
The GCF of 5416,8712 is 8 .
LCM of 788,2756 is 542932.
The greatest common factor of 5416/788,8712/2756 = [GCF of 5416,8712]/[LCM of 788,2756]= 8/542932
Therefore, the GCF of 5416/788,8712/2756 is 8/542932.
To find the highest common factor of 5416,8712, we have to find the factors of both numbers and list the highest common factor.
The factors of 5416 are 1, 2, 4, 8, 677, 1354, 2708, 5416
The factors of 8712 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 18, 22, 24, 33, 36, 44, 66, 72, 88, 99, 121, 132, 198, 242, 264, 363, 396, 484, 726, 792, 968, 1089, 1452, 2178, 2904, 4356, 8712
The HCF of 5416,8712 is 8.
Lets's calculate GCF of 5416,8712
2 | 5416, 8712 |
2 | 2708, 4356 |
2 | 1354, 2178 |
677, 1089 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 5416
:1,2,4,8,677,1354,2708,5416
Now, list down the factors of 8712
:1,2,3,4,6,8,9,11,12,18,22,24,33,36,44,66,72,88,99,121,132,198,242,264,363,396,484,726,792,968,1089,1452,2178,2904,4356,8712
Greatest Common Factor
We found the factors 5416,8712 . The biggest common factor number is the GCF number.
So the greatest common factor 5416,8712 is 8.
Lets's calculate LCM of 788,2756
2 | 788, 2756 |
2 | 394, 1378 |
197, 689 |
∴ So the LCM of the given numbers is 2 x 2 x 197 x 689 = 542932
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/542932
Therefore, the GCF of Fractions 5416/788,8712/2756 is 8/542932
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 788,2756 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(788,2756) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(788,2756) x common factors =4 x 1 = 4
LCM(788,2756) = ( 788 × 2756 ) / 4
LCM(788,2756) = 2171728 / 4
LCM(788,2756) = 542932
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 5416,8712?
The HCF of 5416,8712 is 8
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 5416/788, 8712/2756?
Answer: GCF of Numerators as per given numbers 5416/788, 8712/2756 is
GCF of Numerators i.e. for 5416,8712 is 8
LCM of denominators i.e. for 788,2756 is 542932.
Thus, GCF of Fractions is 8/542932.Finally, GCF of Fractions for 5416/788, 8712/2756 is 8/542932.