Use our free GCF of Fractions Calculator tool to compute the GCF of 348/107, 270/353 i.e 6/37771 easily. The following is the detailed procedure to determine the greatest common factor of fractions 348/107, 270/353.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 348/107,270/353
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 348/107,270/353, numerators are 348,270
Denominators are 107,353
The GCF of 348,270 is 6 .
LCM of 107,353 is 37771.
The greatest common factor of 348/107,270/353 = [GCF of 348,270]/[LCM of 107,353]= 6/37771
Therefore, the GCF of 348/107,270/353 is 6/37771.
To find the highest common factor of 348,270, we have to find the factors of both numbers and list the highest common factor.
The factors of 348 are 1, 2, 3, 4, 6, 12, 29, 58, 87, 116, 174, 348
The factors of 270 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270
The HCF of 348,270 is 6.
Lets's calculate GCF of 348,270
2 | 348, 270 |
3 | 174, 135 |
58, 45 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 348
:1,2,3,4,6,12,29,58,87,116,174,348
Now, list down the factors of 270
:1,2,3,5,6,9,10,15,18,27,30,45,54,90,135,270
Greatest Common Factor
We found the factors 348,270 . The biggest common factor number is the GCF number.
So the greatest common factor 348,270 is 6.
Lets's calculate LCM of 107,353
Given numbers has no common factors except 1. So, there LCM is their product i.e 37771
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/37771
Therefore, the GCF of Fractions 348/107,270/353 is 6/37771
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 107,353 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(107,353) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(107,353) x common factors =1 x 1 = 1
LCM(107,353) = ( 107 × 353 ) / 1
LCM(107,353) = 37771 / 1
LCM(107,353) = 37771
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 348,270?
The HCF of 348,270 is 6
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 348/107, 270/353?
Answer: GCF of Numerators as per given numbers 348/107, 270/353 is
GCF of Numerators i.e. for 348,270 is 6
LCM of denominators i.e. for 107,353 is 37771.
Thus, GCF of Fractions is 6/37771.Finally, GCF of Fractions for 348/107, 270/353 is 6/37771.