Use our free GCF of Fractions Calculator tool to compute the GCF of 82/32, 892/66, 410/149 i.e 2/157344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 82/32, 892/66, 410/149.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 82/32,892/66,410/149
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 82/32,892/66,410/149, numerators are 82,892,410
Denominators are 32,66,149
The GCF of 82,892,410 is 2 .
LCM of 32,66,149 is 157344.
The greatest common factor of 82/32,892/66,410/149 = [GCF of 82,892,410]/[LCM of 32,66,149]= 2/157344
Therefore, the GCF of 82/32,892/66,410/149 is 2/157344.
To find the highest common factor of 82,892,410, we have to find the factors of both numbers and list the highest common factor.
The factors of 82 are 1, 2, 41, 82
The factors of 892 are 1, 2, 4, 223, 446, 892
The factors of 410 are 1, 2, 5, 10, 41, 82, 205, 410
The HCF of 82,892,410 is 2.
Lets's calculate GCF of 82,892,410
2 | 82, 892, 410 |
41, 446, 205 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 82
:1,2,41,82
Now, list down the factors of 892
:1,2,4,223,446,892
Now, list down the factors of 410
:1,2,5,10,41,82,205,410
Greatest Common Factor
We found the factors 82,892,410 . The biggest common factor number is the GCF number.
So the greatest common factor 82,892,410 is 2.
Lets's calculate LCM of 32,66,149
2 | 32, 66, 149 |
16, 33, 149 |
∴ So the LCM of the given numbers is 2 x 16 x 33 x 149 = 157344
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/157344
Therefore, the GCF of Fractions 82/32,892/66,410/149 is 2/157344
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 32,66,149 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,66,149) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(32,66,149) x common factors =1 x 2 = 2
LCM(32,66,149) = ( 32 × 66 × 149 ) / 2
LCM(32,66,149) = 314688 / 2
LCM(32,66,149) = 157344
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 82,892,410?
The HCF of 82,892,410 is 2
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 82/32, 892/66, 410/149?
Answer: GCF of Numerators as per given numbers 82/32, 892/66, 410/149 is
GCF of Numerators i.e. for 82,892,410 is 2
LCM of denominators i.e. for 32,66,149 is 157344.
Thus, GCF of Fractions is 2/157344.Finally, GCF of Fractions for 82/32, 892/66, 410/149 is 2/157344.