Use our free GCF of Fractions Calculator tool to compute the GCF of 648/726, 2184/9720 i.e 24/1176120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 648/726, 2184/9720.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 648/726,2184/9720
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 648/726,2184/9720, numerators are 648,2184
Denominators are 726,9720
The GCF of 648,2184 is 24 .
LCM of 726,9720 is 1176120.
The greatest common factor of 648/726,2184/9720 = [GCF of 648,2184]/[LCM of 726,9720]= 24/1176120
Therefore, the GCF of 648/726,2184/9720 is 24/1176120.
To find the highest common factor of 648,2184, we have to find the factors of both numbers and list the highest common factor.
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 2184 are 1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 273, 312, 364, 546, 728, 1092, 2184
The HCF of 648,2184 is 24.
Lets's calculate GCF of 648,2184
2 | 648, 2184 |
2 | 324, 1092 |
2 | 162, 546 |
3 | 81, 273 |
27, 91 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
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 2184
:1,2,3,4,6,7,8,12,13,14,21,24,26,28,39,42,52,56,78,84,91,104,156,168,182,273,312,364,546,728,1092,2184
Greatest Common Factor
We found the factors 648,2184 . The biggest common factor number is the GCF number.
So the greatest common factor 648,2184 is 24.
Lets's calculate LCM of 726,9720
2 | 726, 9720 |
3 | 363, 4860 |
121, 1620 |
∴ So the LCM of the given numbers is 2 x 3 x 121 x 1620 = 1176120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/1176120
Therefore, the GCF of Fractions 648/726,2184/9720 is 24/1176120
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 726,9720 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(726,9720) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(726,9720) x common factors =6 x 1 = 6
LCM(726,9720) = ( 726 × 9720 ) / 6
LCM(726,9720) = 7056720 / 6
LCM(726,9720) = 1176120
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 648,2184?
The HCF of 648,2184 is 24
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 648/726, 2184/9720?
Answer: GCF of Numerators as per given numbers 648/726, 2184/9720 is
GCF of Numerators i.e. for 648,2184 is 24
LCM of denominators i.e. for 726,9720 is 1176120.
Thus, GCF of Fractions is 24/1176120.Finally, GCF of Fractions for 648/726, 2184/9720 is 24/1176120.