Use our free GCF of Fractions Calculator tool to compute the GCF of 77/156, 560/622, 105/646 i.e 7/15670668 easily. The following is the detailed procedure to determine the greatest common factor of fractions 77/156, 560/622, 105/646.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 77/156,560/622,105/646
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 77/156,560/622,105/646, numerators are 77,560,105
Denominators are 156,622,646
The GCF of 77,560,105 is 7 .
LCM of 156,622,646 is 15670668.
The greatest common factor of 77/156,560/622,105/646 = [GCF of 77,560,105]/[LCM of 156,622,646]= 7/15670668
Therefore, the GCF of 77/156,560/622,105/646 is 7/15670668.
To find the highest common factor of 77,560,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 77 are 1, 7, 11, 77
The factors of 560 are 1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 56, 70, 80, 112, 140, 280, 560
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 77,560,105 is 7.
Lets's calculate GCF of 77,560,105
7 | 77, 560, 105 |
11, 80, 15 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 77
:1,7,11,77
Now, list down the factors of 560
:1,2,4,5,7,8,10,14,16,20,28,35,40,56,70,80,112,140,280,560
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 77,560,105 . The biggest common factor number is the GCF number.
So the greatest common factor 77,560,105 is 7.
Lets's calculate LCM of 156,622,646
2 | 156, 622, 646 |
78, 311, 323 |
∴ So the LCM of the given numbers is 2 x 78 x 311 x 323 = 15670668
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/15670668
Therefore, the GCF of Fractions 77/156,560/622,105/646 is 7/15670668
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 156,622,646 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(156,622,646) = 2
common factors(in case of two or more numbers have common factors) = 2
GCF(156,622,646) x common factors =2 x 2 = 4
LCM(156,622,646) = ( 156 × 622 × 646 ) / 4
LCM(156,622,646) = 62682672 / 4
LCM(156,622,646) = 15670668
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 77,560,105?
The HCF of 77,560,105 is 7
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 77/156, 560/622, 105/646?
Answer: GCF of Numerators as per given numbers 77/156, 560/622, 105/646 is
GCF of Numerators i.e. for 77,560,105 is 7
LCM of denominators i.e. for 156,622,646 is 15670668.
Thus, GCF of Fractions is 7/15670668.Finally, GCF of Fractions for 77/156, 560/622, 105/646 is 7/15670668.