Use our free GCF of Fractions Calculator tool to compute the GCF of 420/213, 309/568 i.e 3/1704 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/213, 309/568.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 420/213,309/568
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 420/213,309/568, numerators are 420,309
Denominators are 213,568
The GCF of 420,309 is 3 .
LCM of 213,568 is 1704.
The greatest common factor of 420/213,309/568 = [GCF of 420,309]/[LCM of 213,568]= 3/1704
Therefore, the GCF of 420/213,309/568 is 3/1704.
To find the highest common factor of 420,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The factors of 309 are 1, 3, 103, 309
The HCF of 420,309 is 3.
Lets's calculate GCF of 420,309
3 | 420, 309 |
140, 103 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 420,309 . The biggest common factor number is the GCF number.
So the greatest common factor 420,309 is 3.
Lets's calculate LCM of 213,568
71 | 213, 568 |
3, 8 |
∴ So the LCM of the given numbers is 71 x 3 x 8 = 1704
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1704
Therefore, the GCF of Fractions 420/213,309/568 is 3/1704
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 213,568 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(213,568) = 71
common factors(in case of two or more numbers have common factors) = 1
GCF(213,568) x common factors =71 x 1 = 71
LCM(213,568) = ( 213 × 568 ) / 71
LCM(213,568) = 120984 / 71
LCM(213,568) = 1704
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 420,309?
The HCF of 420,309 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 420/213, 309/568?
Answer: GCF of Numerators as per given numbers 420/213, 309/568 is
GCF of Numerators i.e. for 420,309 is 3
LCM of denominators i.e. for 213,568 is 1704.
Thus, GCF of Fractions is 3/1704.Finally, GCF of Fractions for 420/213, 309/568 is 3/1704.