Use our free GCF of Fractions Calculator tool to compute the GCF of 7689/228, 9498/1762 i.e 3/200868 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7689/228, 9498/1762.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7689/228,9498/1762
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 7689/228,9498/1762, numerators are 7689,9498
Denominators are 228,1762
The GCF of 7689,9498 is 3 .
LCM of 228,1762 is 200868.
The greatest common factor of 7689/228,9498/1762 = [GCF of 7689,9498]/[LCM of 228,1762]= 3/200868
Therefore, the GCF of 7689/228,9498/1762 is 3/200868.
To find the highest common factor of 7689,9498, we have to find the factors of both numbers and list the highest common factor.
The factors of 7689 are 1, 3, 11, 33, 233, 699, 2563, 7689
The factors of 9498 are 1, 2, 3, 6, 1583, 3166, 4749, 9498
The HCF of 7689,9498 is 3.
Lets's calculate GCF of 7689,9498
3 | 7689, 9498 |
2563, 3166 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 7689
:1,3,11,33,233,699,2563,7689
Now, list down the factors of 9498
:1,2,3,6,1583,3166,4749,9498
Greatest Common Factor
We found the factors 7689,9498 . The biggest common factor number is the GCF number.
So the greatest common factor 7689,9498 is 3.
Lets's calculate LCM of 228,1762
2 | 228, 1762 |
114, 881 |
∴ So the LCM of the given numbers is 2 x 114 x 881 = 200868
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/200868
Therefore, the GCF of Fractions 7689/228,9498/1762 is 3/200868
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 228,1762 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(228,1762) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(228,1762) x common factors =2 x 1 = 2
LCM(228,1762) = ( 228 × 1762 ) / 2
LCM(228,1762) = 401736 / 2
LCM(228,1762) = 200868
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 7689,9498?
The HCF of 7689,9498 is 3
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 7689/228, 9498/1762?
Answer: GCF of Numerators as per given numbers 7689/228, 9498/1762 is
GCF of Numerators i.e. for 7689,9498 is 3
LCM of denominators i.e. for 228,1762 is 200868.
Thus, GCF of Fractions is 3/200868.Finally, GCF of Fractions for 7689/228, 9498/1762 is 3/200868.