Use our free GCF of Fractions Calculator tool to compute the GCF of 110/318, 822/712 i.e 2/113208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 110/318, 822/712.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 110/318,822/712
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 110/318,822/712, numerators are 110,822
Denominators are 318,712
The GCF of 110,822 is 2 .
LCM of 318,712 is 113208.
The greatest common factor of 110/318,822/712 = [GCF of 110,822]/[LCM of 318,712]= 2/113208
Therefore, the GCF of 110/318,822/712 is 2/113208.
To find the highest common factor of 110,822, we have to find the factors of both numbers and list the highest common factor.
The factors of 110 are 1, 2, 5, 10, 11, 22, 55, 110
The factors of 822 are 1, 2, 3, 6, 137, 274, 411, 822
The HCF of 110,822 is 2.
Lets's calculate GCF of 110,822
2 | 110, 822 |
55, 411 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 110
:1,2,5,10,11,22,55,110
Now, list down the factors of 822
:1,2,3,6,137,274,411,822
Greatest Common Factor
We found the factors 110,822 . The biggest common factor number is the GCF number.
So the greatest common factor 110,822 is 2.
Lets's calculate LCM of 318,712
2 | 318, 712 |
159, 356 |
∴ So the LCM of the given numbers is 2 x 159 x 356 = 113208
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/113208
Therefore, the GCF of Fractions 110/318,822/712 is 2/113208
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 318,712 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(318,712) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(318,712) x common factors =2 x 1 = 2
LCM(318,712) = ( 318 × 712 ) / 2
LCM(318,712) = 226416 / 2
LCM(318,712) = 113208
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 110,822?
The HCF of 110,822 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 110/318, 822/712?
Answer: GCF of Numerators as per given numbers 110/318, 822/712 is
GCF of Numerators i.e. for 110,822 is 2
LCM of denominators i.e. for 318,712 is 113208.
Thus, GCF of Fractions is 2/113208.Finally, GCF of Fractions for 110/318, 822/712 is 2/113208.