Use our free GCF of Fractions Calculator tool to compute the GCF of 828/498, 690/857 i.e 138/426786 easily. The following is the detailed procedure to determine the greatest common factor of fractions 828/498, 690/857.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 828/498,690/857
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 828/498,690/857, numerators are 828,690
Denominators are 498,857
The GCF of 828,690 is 138 .
LCM of 498,857 is 426786.
The greatest common factor of 828/498,690/857 = [GCF of 828,690]/[LCM of 498,857]= 138/426786
Therefore, the GCF of 828/498,690/857 is 138/426786.
To find the highest common factor of 828,690, we have to find the factors of both numbers and list the highest common factor.
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The factors of 690 are 1, 2, 3, 5, 6, 10, 15, 23, 30, 46, 69, 115, 138, 230, 345, 690
The HCF of 828,690 is 138.
Lets's calculate GCF of 828,690
2 | 828, 690 |
3 | 414, 345 |
23 | 138, 115 |
6, 5 |
∴ So the GCF of the given numbers is 2 x 3 x 23 = 138
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Now, list down the factors of 690
:1,2,3,5,6,10,15,23,30,46,69,115,138,230,345,690
Greatest Common Factor
We found the factors 828,690 . The biggest common factor number is the GCF number.
So the greatest common factor 828,690 is 138.
Lets's calculate LCM of 498,857
Given numbers has no common factors except 1. So, there LCM is their product i.e 426786
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 138/426786
Therefore, the GCF of Fractions 828/498,690/857 is 138/426786
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 498,857 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(498,857) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(498,857) x common factors =1 x 1 = 1
LCM(498,857) = ( 498 × 857 ) / 1
LCM(498,857) = 426786 / 1
LCM(498,857) = 426786
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 828,690?
The HCF of 828,690 is 138
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 828/498, 690/857?
Answer: GCF of Numerators as per given numbers 828/498, 690/857 is
GCF of Numerators i.e. for 828,690 is 138
LCM of denominators i.e. for 498,857 is 426786.
Thus, GCF of Fractions is 138/426786.Finally, GCF of Fractions for 828/498, 690/857 is 138/426786.