Use our free GCF of Fractions Calculator tool to compute the GCF of 68/30, 362/21, 350/922 i.e 2/96810 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/30, 362/21, 350/922.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 68/30,362/21,350/922
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 68/30,362/21,350/922, numerators are 68,362,350
Denominators are 30,21,922
The GCF of 68,362,350 is 2 .
LCM of 30,21,922 is 96810.
The greatest common factor of 68/30,362/21,350/922 = [GCF of 68,362,350]/[LCM of 30,21,922]= 2/96810
Therefore, the GCF of 68/30,362/21,350/922 is 2/96810.
To find the highest common factor of 68,362,350, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 362 are 1, 2, 181, 362
The factors of 350 are 1, 2, 5, 7, 10, 14, 25, 35, 50, 70, 175, 350
The HCF of 68,362,350 is 2.
Lets's calculate GCF of 68,362,350
2 | 68, 362, 350 |
34, 181, 175 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 362
:1,2,181,362
Now, list down the factors of 350
:1,2,5,7,10,14,25,35,50,70,175,350
Greatest Common Factor
We found the factors 68,362,350 . The biggest common factor number is the GCF number.
So the greatest common factor 68,362,350 is 2.
Lets's calculate LCM of 30,21,922
2 | 30, 21, 922 |
3 | 15, 21, 461 |
5, 7, 461 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 7 x 461 = 96810
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/96810
Therefore, the GCF of Fractions 68/30,362/21,350/922 is 2/96810
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 30,21,922 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,21,922) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(30,21,922) x common factors =1 x 6 = 6
LCM(30,21,922) = ( 30 × 21 × 922 ) / 6
LCM(30,21,922) = 580860 / 6
LCM(30,21,922) = 96810
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 68,362,350?
The HCF of 68,362,350 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 68/30, 362/21, 350/922?
Answer: GCF of Numerators as per given numbers 68/30, 362/21, 350/922 is
GCF of Numerators i.e. for 68,362,350 is 2
LCM of denominators i.e. for 30,21,922 is 96810.
Thus, GCF of Fractions is 2/96810.Finally, GCF of Fractions for 68/30, 362/21, 350/922 is 2/96810.