Use our free GCF of Fractions Calculator tool to compute the GCF of 213/792, 822/782 i.e 3/309672 easily. The following is the detailed procedure to determine the greatest common factor of fractions 213/792, 822/782.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 213/792,822/782
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 213/792,822/782, numerators are 213,822
Denominators are 792,782
The GCF of 213,822 is 3 .
LCM of 792,782 is 309672.
The greatest common factor of 213/792,822/782 = [GCF of 213,822]/[LCM of 792,782]= 3/309672
Therefore, the GCF of 213/792,822/782 is 3/309672.
To find the highest common factor of 213,822, we have to find the factors of both numbers and list the highest common factor.
The factors of 213 are 1, 3, 71, 213
The factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822
The HCF of 213,822 is 3.
Lets's calculate GCF of 213,822
3 | 213, 822 |
71, 274 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 213
:1,3,71,213
Now, list down the factors of 822
:1,2,3,6,137,274,411,822
Greatest Common Factor
We found the factors 213,822 . The biggest common factor number is the GCF number.
So the greatest common factor 213,822 is 3.
Lets's calculate LCM of 792,782
2 | 792, 782 |
396, 391 |
∴ So the LCM of the given numbers is 2 x 396 x 391 = 309672
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/309672
Therefore, the GCF of Fractions 213/792,822/782 is 3/309672
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 792,782 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(792,782) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(792,782) x common factors =2 x 1 = 2
LCM(792,782) = ( 792 × 782 ) / 2
LCM(792,782) = 619344 / 2
LCM(792,782) = 309672
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 213,822?
The HCF of 213,822 is 3
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 213/792, 822/782?
Answer: GCF of Numerators as per given numbers 213/792, 822/782 is
GCF of Numerators i.e. for 213,822 is 3
LCM of denominators i.e. for 792,782 is 309672.
Thus, GCF of Fractions is 3/309672.Finally, GCF of Fractions for 213/792, 822/782 is 3/309672.