Use our free GCF of Fractions Calculator tool to compute the GCF of 14/21, 214/37, 670/983 i.e 2/763791 easily. The following is the detailed procedure to determine the greatest common factor of fractions 14/21, 214/37, 670/983.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 14/21,214/37,670/983
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 14/21,214/37,670/983, numerators are 14,214,670
Denominators are 21,37,983
The GCF of 14,214,670 is 2 .
LCM of 21,37,983 is 763791.
The greatest common factor of 14/21,214/37,670/983 = [GCF of 14,214,670]/[LCM of 21,37,983]= 2/763791
Therefore, the GCF of 14/21,214/37,670/983 is 2/763791.
To find the highest common factor of 14,214,670, we have to find the factors of both numbers and list the highest common factor.
The factors of 14 are 1, 2, 7, 14
The factors of 214 are 1, 2, 107, 214
The factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670
The HCF of 14,214,670 is 2.
Lets's calculate GCF of 14,214,670
2 | 14, 214, 670 |
7, 107, 335 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 214
:1,2,107,214
Now, list down the factors of 670
:1,2,5,10,67,134,335,670
Greatest Common Factor
We found the factors 14,214,670 . The biggest common factor number is the GCF number.
So the greatest common factor 14,214,670 is 2.
Lets's calculate LCM of 21,37,983
Given numbers has no common factors except 1. So, there LCM is their product i.e 763791
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/763791
Therefore, the GCF of Fractions 14/21,214/37,670/983 is 2/763791
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 21,37,983 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,37,983) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(21,37,983) x common factors =1 x 1 = 1
LCM(21,37,983) = ( 21 × 37 × 983 ) / 1
LCM(21,37,983) = 763791 / 1
LCM(21,37,983) = 763791
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 14,214,670?
The HCF of 14,214,670 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 14/21, 214/37, 670/983?
Answer: GCF of Numerators as per given numbers 14/21, 214/37, 670/983 is
GCF of Numerators i.e. for 14,214,670 is 2
LCM of denominators i.e. for 21,37,983 is 763791.
Thus, GCF of Fractions is 2/763791.Finally, GCF of Fractions for 14/21, 214/37, 670/983 is 2/763791.