Use our free GCF of Fractions Calculator tool to compute the GCF of 821/490, 830/338 i.e 1/82810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 821/490, 830/338.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 821/490,830/338
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 821/490,830/338, numerators are 821,830
Denominators are 490,338
The GCF of 821,830 is 1 .
LCM of 490,338 is 82810.
The greatest common factor of 821/490,830/338 = [GCF of 821,830]/[LCM of 490,338]= 1/82810
Therefore, the GCF of 821/490,830/338 is 1/82810.
To find the highest common factor of 821,830, we have to find the factors of both numbers and list the highest common factor.
The factors of 821 are 1, 821
The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830
The HCF of 821,830 is 1.
Lets's calculate GCF of 821,830
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 821
:1,821
Now, list down the factors of 830
:1,2,5,10,83,166,415,830
Greatest Common Factor
We found the factors 821,830 . The biggest common factor number is the GCF number.
So the greatest common factor 821,830 is 1.
Lets's calculate LCM of 490,338
2 | 490, 338 |
245, 169 |
∴ So the LCM of the given numbers is 2 x 245 x 169 = 82810
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/82810
Therefore, the GCF of Fractions 821/490,830/338 is 1/82810
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 490,338 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(490,338) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(490,338) x common factors =2 x 1 = 2
LCM(490,338) = ( 490 × 338 ) / 2
LCM(490,338) = 165620 / 2
LCM(490,338) = 82810
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 821,830?
The HCF of 821,830 is 1
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 821/490, 830/338?
Answer: GCF of Numerators as per given numbers 821/490, 830/338 is
GCF of Numerators i.e. for 821,830 is 1
LCM of denominators i.e. for 490,338 is 82810.
Thus, GCF of Fractions is 1/82810.Finally, GCF of Fractions for 821/490, 830/338 is 1/82810.