Use our free GCF of Fractions Calculator tool to compute the GCF of 984/455, 410/351 i.e 82/12285 easily. The following is the detailed procedure to determine the greatest common factor of fractions 984/455, 410/351.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 984/455,410/351
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 984/455,410/351, numerators are 984,410
Denominators are 455,351
The GCF of 984,410 is 82 .
LCM of 455,351 is 12285.
The greatest common factor of 984/455,410/351 = [GCF of 984,410]/[LCM of 455,351]= 82/12285
Therefore, the GCF of 984/455,410/351 is 82/12285.
To find the highest common factor of 984,410, we have to find the factors of both numbers and list the highest common factor.
The factors of 984 are 1, 2, 3, 4, 6, 8, 12, 24, 41, 82, 123, 164, 246, 328, 492, 984
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The HCF of 984,410 is 82.
Lets's calculate GCF of 984,410
2 | 984, 410 |
41 | 492, 205 |
12, 5 |
∴ So the GCF of the given numbers is 2 x 41 = 82
Now, list down the factors of 984
:1,2,3,4,6,8,12,24,41,82,123,164,246,328,492,984
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Greatest Common Factor
We found the factors 984,410 . The biggest common factor number is the GCF number.
So the greatest common factor 984,410 is 82.
Lets's calculate LCM of 455,351
13 | 455, 351 |
35, 27 |
∴ So the LCM of the given numbers is 13 x 35 x 27 = 12285
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 82/12285
Therefore, the GCF of Fractions 984/455,410/351 is 82/12285
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 455,351 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(455,351) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(455,351) x common factors =13 x 1 = 13
LCM(455,351) = ( 455 × 351 ) / 13
LCM(455,351) = 159705 / 13
LCM(455,351) = 12285
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 984,410?
The HCF of 984,410 is 82
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 984/455, 410/351?
Answer: GCF of Numerators as per given numbers 984/455, 410/351 is
GCF of Numerators i.e. for 984,410 is 82
LCM of denominators i.e. for 455,351 is 12285.
Thus, GCF of Fractions is 82/12285.Finally, GCF of Fractions for 984/455, 410/351 is 82/12285.