Use our free GCF of Fractions Calculator tool to compute the GCF of 431/301, 4194/280 i.e 1/12040 easily. The following is the detailed procedure to determine the greatest common factor of fractions 431/301, 4194/280.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 431/301,4194/280
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 431/301,4194/280, numerators are 431,4194
Denominators are 301,280
The GCF of 431,4194 is 1 .
LCM of 301,280 is 12040.
The greatest common factor of 431/301,4194/280 = [GCF of 431,4194]/[LCM of 301,280]= 1/12040
Therefore, the GCF of 431/301,4194/280 is 1/12040.
To find the highest common factor of 431,4194, we have to find the factors of both numbers and list the highest common factor.
The factors of 431 are 1, 431
The factors of 4194 are 1, 2, 3, 6, 9, 18, 233, 466, 699, 1398, 2097, 4194
The HCF of 431,4194 is 1.
Lets's calculate GCF of 431,4194
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 431
:1,431
Now, list down the factors of 4194
:1,2,3,6,9,18,233,466,699,1398,2097,4194
Greatest Common Factor
We found the factors 431,4194 . The biggest common factor number is the GCF number.
So the greatest common factor 431,4194 is 1.
Lets's calculate LCM of 301,280
7 | 301, 280 |
43, 40 |
∴ So the LCM of the given numbers is 7 x 43 x 40 = 12040
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12040
Therefore, the GCF of Fractions 431/301,4194/280 is 1/12040
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 301,280 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(301,280) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(301,280) x common factors =7 x 1 = 7
LCM(301,280) = ( 301 × 280 ) / 7
LCM(301,280) = 84280 / 7
LCM(301,280) = 12040
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 431,4194?
The HCF of 431,4194 is 1
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 431/301, 4194/280?
Answer: GCF of Numerators as per given numbers 431/301, 4194/280 is
GCF of Numerators i.e. for 431,4194 is 1
LCM of denominators i.e. for 301,280 is 12040.
Thus, GCF of Fractions is 1/12040.Finally, GCF of Fractions for 431/301, 4194/280 is 1/12040.