Use our free GCF of Fractions Calculator tool to compute the GCF of 30/269, 60/7285 i.e 30/1959665 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/269, 60/7285.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 30/269,60/7285
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 30/269,60/7285, numerators are 30,60
Denominators are 269,7285
The GCF of 30,60 is 30 .
LCM of 269,7285 is 1959665.
The greatest common factor of 30/269,60/7285 = [GCF of 30,60]/[LCM of 269,7285]= 30/1959665
Therefore, the GCF of 30/269,60/7285 is 30/1959665.
To find the highest common factor of 30,60, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
The HCF of 30,60 is 30.
Lets's calculate GCF of 30,60
2 | 30, 60 |
3 | 15, 30 |
5 | 5, 10 |
1, 2 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 60
:1,2,3,4,5,6,10,12,15,20,30,60
Greatest Common Factor
We found the factors 30,60 . The biggest common factor number is the GCF number.
So the greatest common factor 30,60 is 30.
Lets's calculate LCM of 269,7285
Given numbers has no common factors except 1. So, there LCM is their product i.e 1959665
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/1959665
Therefore, the GCF of Fractions 30/269,60/7285 is 30/1959665
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 269,7285 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(269,7285) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(269,7285) x common factors =1 x 1 = 1
LCM(269,7285) = ( 269 × 7285 ) / 1
LCM(269,7285) = 1959665 / 1
LCM(269,7285) = 1959665
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 30,60?
The HCF of 30,60 is 30
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 30/269, 60/7285?
Answer: GCF of Numerators as per given numbers 30/269, 60/7285 is
GCF of Numerators i.e. for 30,60 is 30
LCM of denominators i.e. for 269,7285 is 1959665.
Thus, GCF of Fractions is 30/1959665.Finally, GCF of Fractions for 30/269, 60/7285 is 30/1959665.