Use our free GCF of Fractions Calculator tool to compute the GCF of 202/370, 310/590 i.e 2/21830 easily. The following is the detailed procedure to determine the greatest common factor of fractions 202/370, 310/590.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 202/370,310/590
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 202/370,310/590, numerators are 202,310
Denominators are 370,590
The GCF of 202,310 is 2 .
LCM of 370,590 is 21830.
The greatest common factor of 202/370,310/590 = [GCF of 202,310]/[LCM of 370,590]= 2/21830
Therefore, the GCF of 202/370,310/590 is 2/21830.
To find the highest common factor of 202,310, we have to find the factors of both numbers and list the highest common factor.
The factors of 202 are 1, 2, 101, 202
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The HCF of 202,310 is 2.
Lets's calculate GCF of 202,310
2 | 202, 310 |
101, 155 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 202
:1,2,101,202
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Greatest Common Factor
We found the factors 202,310 . The biggest common factor number is the GCF number.
So the greatest common factor 202,310 is 2.
Lets's calculate LCM of 370,590
2 | 370, 590 |
5 | 185, 295 |
37, 59 |
∴ So the LCM of the given numbers is 2 x 5 x 37 x 59 = 21830
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/21830
Therefore, the GCF of Fractions 202/370,310/590 is 2/21830
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 370,590 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(370,590) = 10
common factors(in case of two or more numbers have common factors) = 1
GCF(370,590) x common factors =10 x 1 = 10
LCM(370,590) = ( 370 × 590 ) / 10
LCM(370,590) = 218300 / 10
LCM(370,590) = 21830
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 202,310?
The HCF of 202,310 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 202/370, 310/590?
Answer: GCF of Numerators as per given numbers 202/370, 310/590 is
GCF of Numerators i.e. for 202,310 is 2
LCM of denominators i.e. for 370,590 is 21830.
Thus, GCF of Fractions is 2/21830.Finally, GCF of Fractions for 202/370, 310/590 is 2/21830.