GCF of 109/309, 249/225
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 109/309, 249/225 i.e 1/23175 easily. The following is the detailed procedure to determine the greatest common factor of fractions 109/309, 249/225.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 109/309,249/225?
Given fractions are 109/309,249/225
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 109/309,249/225, numerators are 109,249
Denominators are 309,225
The GCF of 109,249 is 1 .
LCM of 309,225 is 23175.
The greatest common factor of 109/309,249/225 = [GCF of 109,249]/[LCM of 309,225]= 1/23175
Therefore, the GCF of 109/309,249/225 is 1/23175.
To find the highest common factor of 109,249, we have to find the factors of both numbers and list the highest common factor.
The factors of 109 are 1, 109
The factors of 249 are 1, 3, 83, 249
The HCF of 109,249 is 1.
Lets's calculate GCF of 109,249
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 109,249 By Matching Biggest Common Factor Method
Now, list down the factors of 109
:1,109
Now, list down the factors of 249
:1,3,83,249
Greatest Common Factor
We found the factors 109,249 . The biggest common factor number is the GCF number.
So the greatest common factor 109,249 is 1.
Lets's calculate LCM of 309,225
| 3 | 309, 225 |
| 103, 75 |
∴ So the LCM of the given numbers is 3 x 103 x 75 = 23175
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23175
Therefore, the GCF of Fractions 109/309,249/225 is 1/23175
Least Common Multiple of 309,225 with GCF Formula
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 309,225 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,225) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,225) x common factors =3 x 1 = 3
LCM(309,225) = ( 309 × 225 ) / 3
LCM(309,225) = 69525 / 3
LCM(309,225) = 23175
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FAQs on GCF of Fractions of 109/309, 249/225
1. What is the HCF of 109,249?
The HCF of 109,249 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 109/309, 249/225?
Answer: GCF of Numerators as per given numbers 109/309, 249/225 is
GCF of Numerators i.e. for 109,249 is 1
LCM of denominators i.e. for 309,225 is 23175.
Thus, GCF of Fractions is 1/23175.Finally, GCF of Fractions for 109/309, 249/225 is 1/23175.