Use our free GCF of Fractions Calculator tool to compute the GCF of 660/458, 542/109 i.e 2/49922 easily. The following is the detailed procedure to determine the greatest common factor of fractions 660/458, 542/109.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 660/458,542/109
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 660/458,542/109, numerators are 660,542
Denominators are 458,109
The GCF of 660,542 is 2 .
LCM of 458,109 is 49922.
The greatest common factor of 660/458,542/109 = [GCF of 660,542]/[LCM of 458,109]= 2/49922
Therefore, the GCF of 660/458,542/109 is 2/49922.
To find the highest common factor of 660,542, 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 542 are 1, 2, 271, 542
The HCF of 660,542 is 2.
Lets's calculate GCF of 660,542
2 | 660, 542 |
330, 271 |
∴ So the GCF of the given numbers is 2 = 2
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 542
:1,2,271,542
Greatest Common Factor
We found the factors 660,542 . The biggest common factor number is the GCF number.
So the greatest common factor 660,542 is 2.
Lets's calculate LCM of 458,109
Given numbers has no common factors except 1. So, there LCM is their product i.e 49922
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/49922
Therefore, the GCF of Fractions 660/458,542/109 is 2/49922
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 458,109 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(458,109) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(458,109) x common factors =1 x 1 = 1
LCM(458,109) = ( 458 × 109 ) / 1
LCM(458,109) = 49922 / 1
LCM(458,109) = 49922
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 660,542?
The HCF of 660,542 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 660/458, 542/109?
Answer: GCF of Numerators as per given numbers 660/458, 542/109 is
GCF of Numerators i.e. for 660,542 is 2
LCM of denominators i.e. for 458,109 is 49922.
Thus, GCF of Fractions is 2/49922.Finally, GCF of Fractions for 660/458, 542/109 is 2/49922.