Use our free GCF of Fractions Calculator tool to compute the GCF of 180/155, 414/289 i.e 18/44795 easily. The following is the detailed procedure to determine the greatest common factor of fractions 180/155, 414/289.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 180/155,414/289
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 180/155,414/289, numerators are 180,414
Denominators are 155,289
The GCF of 180,414 is 18 .
LCM of 155,289 is 44795.
The greatest common factor of 180/155,414/289 = [GCF of 180,414]/[LCM of 155,289]= 18/44795
Therefore, the GCF of 180/155,414/289 is 18/44795.
To find the highest common factor of 180,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 180,414 is 18.
Lets's calculate GCF of 180,414
2 | 180, 414 |
3 | 90, 207 |
3 | 30, 69 |
10, 23 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
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
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 180,414 . The biggest common factor number is the GCF number.
So the greatest common factor 180,414 is 18.
Lets's calculate LCM of 155,289
Given numbers has no common factors except 1. So, there LCM is their product i.e 44795
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/44795
Therefore, the GCF of Fractions 180/155,414/289 is 18/44795
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 155,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(155,289) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(155,289) x common factors =1 x 1 = 1
LCM(155,289) = ( 155 × 289 ) / 1
LCM(155,289) = 44795 / 1
LCM(155,289) = 44795
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 180,414?
The HCF of 180,414 is 18
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 180/155, 414/289?
Answer: GCF of Numerators as per given numbers 180/155, 414/289 is
GCF of Numerators i.e. for 180,414 is 18
LCM of denominators i.e. for 155,289 is 44795.
Thus, GCF of Fractions is 18/44795.Finally, GCF of Fractions for 180/155, 414/289 is 18/44795.