Use our free GCF of Fractions Calculator tool to compute the GCF of 80/96, 648/84, 312/717 i.e 8/160608 easily. The following is the detailed procedure to determine the greatest common factor of fractions 80/96, 648/84, 312/717.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 80/96,648/84,312/717
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 80/96,648/84,312/717, numerators are 80,648,312
Denominators are 96,84,717
The GCF of 80,648,312 is 8 .
LCM of 96,84,717 is 160608.
The greatest common factor of 80/96,648/84,312/717 = [GCF of 80,648,312]/[LCM of 96,84,717]= 8/160608
Therefore, the GCF of 80/96,648/84,312/717 is 8/160608.
To find the highest common factor of 80,648,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 648 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 81, 108, 162, 216, 324, 648
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 80,648,312 is 8.
Lets's calculate GCF of 80,648,312
2 | 80, 648, 312 |
2 | 40, 324, 156 |
2 | 20, 162, 78 |
10, 81, 39 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 648
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,81,108,162,216,324,648
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 80,648,312 . The biggest common factor number is the GCF number.
So the greatest common factor 80,648,312 is 8.
Lets's calculate LCM of 96,84,717
2 | 96, 84, 717 |
2 | 48, 42, 717 |
3 | 24, 21, 717 |
8, 7, 239 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 8 x 7 x 239 = 160608
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/160608
Therefore, the GCF of Fractions 80/96,648/84,312/717 is 8/160608
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 96,84,717 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,84,717) = 3
common factors(in case of two or more numbers have common factors) = 12
GCF(96,84,717) x common factors =3 x 12 = 36
LCM(96,84,717) = ( 96 × 84 × 717 ) / 36
LCM(96,84,717) = 5781888 / 36
LCM(96,84,717) = 160608
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 80,648,312?
The HCF of 80,648,312 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 80/96, 648/84, 312/717?
Answer: GCF of Numerators as per given numbers 80/96, 648/84, 312/717 is
GCF of Numerators i.e. for 80,648,312 is 8
LCM of denominators i.e. for 96,84,717 is 160608.
Thus, GCF of Fractions is 8/160608.Finally, GCF of Fractions for 80/96, 648/84, 312/717 is 8/160608.