Use our free GCF of Fractions Calculator tool to compute the GCF of 1008/384, 2064/576 i.e 48/1152 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1008/384, 2064/576.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 1008/384,2064/576
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 1008/384,2064/576, numerators are 1008,2064
Denominators are 384,576
The GCF of 1008,2064 is 48 .
LCM of 384,576 is 1152.
The greatest common factor of 1008/384,2064/576 = [GCF of 1008,2064]/[LCM of 384,576]= 48/1152
Therefore, the GCF of 1008/384,2064/576 is 48/1152.
To find the highest common factor of 1008,2064, we have to find the factors of both numbers and list the highest common factor.
The factors of 1008 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 36, 42, 48, 56, 63, 72, 84, 112, 126, 144, 168, 252, 336, 504, 1008
The factors of 2064 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 43, 48, 86, 129, 172, 258, 344, 516, 688, 1032, 2064
The HCF of 1008,2064 is 48.
Lets's calculate GCF of 1008,2064
2 | 1008, 2064 |
2 | 504, 1032 |
2 | 252, 516 |
2 | 126, 258 |
3 | 63, 129 |
21, 43 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 = 48
Now, list down the factors of 1008
:1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,36,42,48,56,63,72,84,112,126,144,168,252,336,504,1008
Now, list down the factors of 2064
:1,2,3,4,6,8,12,16,24,43,48,86,129,172,258,344,516,688,1032,2064
Greatest Common Factor
We found the factors 1008,2064 . The biggest common factor number is the GCF number.
So the greatest common factor 1008,2064 is 48.
Lets's calculate LCM of 384,576
2 | 384, 576 |
2 | 192, 288 |
2 | 96, 144 |
2 | 48, 72 |
2 | 24, 36 |
2 | 12, 18 |
3 | 6, 9 |
2, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 3 x 2 x 3 = 1152
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 48/1152
Therefore, the GCF of Fractions 1008/384,2064/576 is 48/1152
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 384,576 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(384,576) = 192
common factors(in case of two or more numbers have common factors) = 1
GCF(384,576) x common factors =192 x 1 = 192
LCM(384,576) = ( 384 × 576 ) / 192
LCM(384,576) = 221184 / 192
LCM(384,576) = 1152
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 1008,2064?
The HCF of 1008,2064 is 48
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 1008/384, 2064/576?
Answer: GCF of Numerators as per given numbers 1008/384, 2064/576 is
GCF of Numerators i.e. for 1008,2064 is 48
LCM of denominators i.e. for 384,576 is 1152.
Thus, GCF of Fractions is 48/1152.Finally, GCF of Fractions for 1008/384, 2064/576 is 48/1152.