Use our free GCF of Fractions Calculator tool to compute the GCF of 660/307, 438/254 i.e 6/77978 easily. The following is the detailed procedure to determine the greatest common factor of fractions 660/307, 438/254.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 660/307,438/254
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 660/307,438/254, numerators are 660,438
Denominators are 307,254
The GCF of 660,438 is 6 .
LCM of 307,254 is 77978.
The greatest common factor of 660/307,438/254 = [GCF of 660,438]/[LCM of 307,254]= 6/77978
Therefore, the GCF of 660/307,438/254 is 6/77978.
To find the highest common factor of 660,438, we have to find the factors of both numbers and list the highest common factor.
The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
The factors of 438 are 1, 2, 3, 6, 73, 146, 219, 438
The HCF of 660,438 is 6.
Lets's calculate GCF of 660,438
2 | 660, 438 |
3 | 330, 219 |
110, 73 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Now, list down the factors of 660
:1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660
Now, list down the factors of 438
:1,2,3,6,73,146,219,438
Greatest Common Factor
We found the factors 660,438 . The biggest common factor number is the GCF number.
So the greatest common factor 660,438 is 6.
Lets's calculate LCM of 307,254
Given numbers has no common factors except 1. So, there LCM is their product i.e 77978
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/77978
Therefore, the GCF of Fractions 660/307,438/254 is 6/77978
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 307,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(307,254) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(307,254) x common factors =1 x 1 = 1
LCM(307,254) = ( 307 × 254 ) / 1
LCM(307,254) = 77978 / 1
LCM(307,254) = 77978
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 660,438?
The HCF of 660,438 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 660/307, 438/254?
Answer: GCF of Numerators as per given numbers 660/307, 438/254 is
GCF of Numerators i.e. for 660,438 is 6
LCM of denominators i.e. for 307,254 is 77978.
Thus, GCF of Fractions is 6/77978.Finally, GCF of Fractions for 660/307, 438/254 is 6/77978.