Use our free GCF of Fractions Calculator tool to compute the GCF of 768/153, 954/578 i.e 6/5202 easily. The following is the detailed procedure to determine the greatest common factor of fractions 768/153, 954/578.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 768/153,954/578
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 768/153,954/578, numerators are 768,954
Denominators are 153,578
The GCF of 768,954 is 6 .
LCM of 153,578 is 5202.
The greatest common factor of 768/153,954/578 = [GCF of 768,954]/[LCM of 153,578]= 6/5202
Therefore, the GCF of 768/153,954/578 is 6/5202.
To find the highest common factor of 768,954, we have to find the factors of both numbers and list the highest common factor.
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The factors of 954 are 1, 2, 3, 6, 9, 18, 53, 106, 159, 318, 477, 954
The HCF of 768,954 is 6.
Lets's calculate GCF of 768,954
2 | 768, 954 |
3 | 384, 477 |
128, 159 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Now, list down the factors of 954
:1,2,3,6,9,18,53,106,159,318,477,954
Greatest Common Factor
We found the factors 768,954 . The biggest common factor number is the GCF number.
So the greatest common factor 768,954 is 6.
Lets's calculate LCM of 153,578
17 | 153, 578 |
9, 34 |
∴ So the LCM of the given numbers is 17 x 9 x 34 = 5202
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/5202
Therefore, the GCF of Fractions 768/153,954/578 is 6/5202
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 153,578 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(153,578) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(153,578) x common factors =17 x 1 = 17
LCM(153,578) = ( 153 × 578 ) / 17
LCM(153,578) = 88434 / 17
LCM(153,578) = 5202
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 768,954?
The HCF of 768,954 is 6
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 768/153, 954/578?
Answer: GCF of Numerators as per given numbers 768/153, 954/578 is
GCF of Numerators i.e. for 768,954 is 6
LCM of denominators i.e. for 153,578 is 5202.
Thus, GCF of Fractions is 6/5202.Finally, GCF of Fractions for 768/153, 954/578 is 6/5202.