Use our free GCF of Fractions Calculator tool to compute the GCF of 27/29, 120/23, 280/104 i.e 1/69368 easily. The following is the detailed procedure to determine the greatest common factor of fractions 27/29, 120/23, 280/104.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 27/29,120/23,280/104
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 27/29,120/23,280/104, numerators are 27,120,280
Denominators are 29,23,104
The GCF of 27,120,280 is 1 .
LCM of 29,23,104 is 69368.
The greatest common factor of 27/29,120/23,280/104 = [GCF of 27,120,280]/[LCM of 29,23,104]= 1/69368
Therefore, the GCF of 27/29,120/23,280/104 is 1/69368.
To find the highest common factor of 27,120,280, we have to find the factors of both numbers and list the highest common factor.
The factors of 27 are 1, 3, 9, 27
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The HCF of 27,120,280 is 1.
Lets's calculate GCF of 27,120,280
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 27
:1,3,9,27
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 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Greatest Common Factor
We found the factors 27,120,280 . The biggest common factor number is the GCF number.
So the greatest common factor 27,120,280 is 1.
Lets's calculate LCM of 29,23,104
Given numbers has no common factors except 1. So, there LCM is their product i.e 69368
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/69368
Therefore, the GCF of Fractions 27/29,120/23,280/104 is 1/69368
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 29,23,104 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(29,23,104) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(29,23,104) x common factors =1 x 1 = 1
LCM(29,23,104) = ( 29 × 23 × 104 ) / 1
LCM(29,23,104) = 69368 / 1
LCM(29,23,104) = 69368
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 27,120,280?
The HCF of 27,120,280 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 27/29, 120/23, 280/104?
Answer: GCF of Numerators as per given numbers 27/29, 120/23, 280/104 is
GCF of Numerators i.e. for 27,120,280 is 1
LCM of denominators i.e. for 29,23,104 is 69368.
Thus, GCF of Fractions is 1/69368.Finally, GCF of Fractions for 27/29, 120/23, 280/104 is 1/69368.