Use our free GCF of Fractions Calculator tool to compute the GCF of 120/509, 180/610 i.e 60/310490 easily. The following is the detailed procedure to determine the greatest common factor of fractions 120/509, 180/610.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 120/509,180/610
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 120/509,180/610, numerators are 120,180
Denominators are 509,610
The GCF of 120,180 is 60 .
LCM of 509,610 is 310490.
The greatest common factor of 120/509,180/610 = [GCF of 120,180]/[LCM of 509,610]= 60/310490
Therefore, the GCF of 120/509,180/610 is 60/310490.
To find the highest common factor of 120,180, we have to find the factors of both numbers and list the highest common factor.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The HCF of 120,180 is 60.
Lets's calculate GCF of 120,180
2 | 120, 180 |
2 | 60, 90 |
3 | 30, 45 |
5 | 10, 15 |
2, 3 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Now, list down the factors of 180
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
Greatest Common Factor
We found the factors 120,180 . The biggest common factor number is the GCF number.
So the greatest common factor 120,180 is 60.
Lets's calculate LCM of 509,610
Given numbers has no common factors except 1. So, there LCM is their product i.e 310490
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/310490
Therefore, the GCF of Fractions 120/509,180/610 is 60/310490
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 509,610 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(509,610) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(509,610) x common factors =1 x 1 = 1
LCM(509,610) = ( 509 × 610 ) / 1
LCM(509,610) = 310490 / 1
LCM(509,610) = 310490
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 120,180?
The HCF of 120,180 is 60
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 120/509, 180/610?
Answer: GCF of Numerators as per given numbers 120/509, 180/610 is
GCF of Numerators i.e. for 120,180 is 60
LCM of denominators i.e. for 509,610 is 310490.
Thus, GCF of Fractions is 60/310490.Finally, GCF of Fractions for 120/509, 180/610 is 60/310490.