Use our free GCF of Fractions Calculator tool to compute the GCF of 460/676, 230/634 i.e 230/214292 easily. The following is the detailed procedure to determine the greatest common factor of fractions 460/676, 230/634.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 460/676,230/634
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 460/676,230/634, numerators are 460,230
Denominators are 676,634
The GCF of 460,230 is 230 .
LCM of 676,634 is 214292.
The greatest common factor of 460/676,230/634 = [GCF of 460,230]/[LCM of 676,634]= 230/214292
Therefore, the GCF of 460/676,230/634 is 230/214292.
To find the highest common factor of 460,230, we have to find the factors of both numbers and list the highest common factor.
The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230
The HCF of 460,230 is 230.
Lets's calculate GCF of 460,230
2 | 460, 230 |
5 | 230, 115 |
23 | 46, 23 |
2, 1 |
∴ So the GCF of the given numbers is 2 x 5 x 23 = 230
Now, list down the factors of 460
:1,2,4,5,10,20,23,46,92,115,230,460
Now, list down the factors of 230
:1,2,5,10,23,46,115,230
Greatest Common Factor
We found the factors 460,230 . The biggest common factor number is the GCF number.
So the greatest common factor 460,230 is 230.
Lets's calculate LCM of 676,634
2 | 676, 634 |
338, 317 |
∴ So the LCM of the given numbers is 2 x 338 x 317 = 214292
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 230/214292
Therefore, the GCF of Fractions 460/676,230/634 is 230/214292
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 676,634 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(676,634) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(676,634) x common factors =2 x 1 = 2
LCM(676,634) = ( 676 × 634 ) / 2
LCM(676,634) = 428584 / 2
LCM(676,634) = 214292
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 460,230?
The HCF of 460,230 is 230
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 460/676, 230/634?
Answer: GCF of Numerators as per given numbers 460/676, 230/634 is
GCF of Numerators i.e. for 460,230 is 230
LCM of denominators i.e. for 676,634 is 214292.
Thus, GCF of Fractions is 230/214292.Finally, GCF of Fractions for 460/676, 230/634 is 230/214292.