Use our free GCF of Fractions Calculator tool to compute the GCF of 7209/235, 8721/5225 i.e 27/245575 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7209/235, 8721/5225.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 7209/235,8721/5225
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 7209/235,8721/5225, numerators are 7209,8721
Denominators are 235,5225
The GCF of 7209,8721 is 27 .
LCM of 235,5225 is 245575.
The greatest common factor of 7209/235,8721/5225 = [GCF of 7209,8721]/[LCM of 235,5225]= 27/245575
Therefore, the GCF of 7209/235,8721/5225 is 27/245575.
To find the highest common factor of 7209,8721, we have to find the factors of both numbers and list the highest common factor.
The factors of 7209 are 1, 3, 9, 27, 81, 89, 267, 801, 2403, 7209
The factors of 8721 are 1, 3, 9, 17, 19, 27, 51, 57, 153, 171, 323, 459, 513, 969, 2907, 8721
The HCF of 7209,8721 is 27.
Lets's calculate GCF of 7209,8721
3 | 7209, 8721 |
3 | 2403, 2907 |
3 | 801, 969 |
267, 323 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Now, list down the factors of 7209
:1,3,9,27,81,89,267,801,2403,7209
Now, list down the factors of 8721
:1,3,9,17,19,27,51,57,153,171,323,459,513,969,2907,8721
Greatest Common Factor
We found the factors 7209,8721 . The biggest common factor number is the GCF number.
So the greatest common factor 7209,8721 is 27.
Lets's calculate LCM of 235,5225
5 | 235, 5225 |
47, 1045 |
∴ So the LCM of the given numbers is 5 x 47 x 1045 = 245575
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/245575
Therefore, the GCF of Fractions 7209/235,8721/5225 is 27/245575
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 235,5225 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(235,5225) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(235,5225) x common factors =5 x 1 = 5
LCM(235,5225) = ( 235 × 5225 ) / 5
LCM(235,5225) = 1227875 / 5
LCM(235,5225) = 245575
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 7209,8721?
The HCF of 7209,8721 is 27
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 7209/235, 8721/5225?
Answer: GCF of Numerators as per given numbers 7209/235, 8721/5225 is
GCF of Numerators i.e. for 7209,8721 is 27
LCM of denominators i.e. for 235,5225 is 245575.
Thus, GCF of Fractions is 27/245575.Finally, GCF of Fractions for 7209/235, 8721/5225 is 27/245575.