Use our free GCF of Fractions Calculator tool to compute the GCF of 812/265, 342/455 i.e 2/24115 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/265, 342/455.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 812/265,342/455
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 812/265,342/455, numerators are 812,342
Denominators are 265,455
The GCF of 812,342 is 2 .
LCM of 265,455 is 24115.
The greatest common factor of 812/265,342/455 = [GCF of 812,342]/[LCM of 265,455]= 2/24115
Therefore, the GCF of 812/265,342/455 is 2/24115.
To find the highest common factor of 812,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 812,342 is 2.
Lets's calculate GCF of 812,342
2 | 812, 342 |
406, 171 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 812,342 . The biggest common factor number is the GCF number.
So the greatest common factor 812,342 is 2.
Lets's calculate LCM of 265,455
5 | 265, 455 |
53, 91 |
∴ So the LCM of the given numbers is 5 x 53 x 91 = 24115
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/24115
Therefore, the GCF of Fractions 812/265,342/455 is 2/24115
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 265,455 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(265,455) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(265,455) x common factors =5 x 1 = 5
LCM(265,455) = ( 265 × 455 ) / 5
LCM(265,455) = 120575 / 5
LCM(265,455) = 24115
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 812,342?
The HCF of 812,342 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 812/265, 342/455?
Answer: GCF of Numerators as per given numbers 812/265, 342/455 is
GCF of Numerators i.e. for 812,342 is 2
LCM of denominators i.e. for 265,455 is 24115.
Thus, GCF of Fractions is 2/24115.Finally, GCF of Fractions for 812/265, 342/455 is 2/24115.