GCF of 2409/144, 9126/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2409/144, 9126/419 i.e 3/60336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2409/144, 9126/419.
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 2409/144,9126/419?
Given fractions are 2409/144,9126/419
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 2409/144,9126/419, numerators are 2409,9126
Denominators are 144,419
The GCF of 2409,9126 is 3 .
LCM of 144,419 is 60336.
The greatest common factor of 2409/144,9126/419 = [GCF of 2409,9126]/[LCM of 144,419]= 3/60336
Therefore, the GCF of 2409/144,9126/419 is 3/60336.
To find the highest common factor of 2409,9126, we have to find the factors of both numbers and list the highest common factor.
The factors of 2409 are 1, 3, 11, 33, 73, 219, 803, 2409
The factors of 9126 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 169, 234, 338, 351, 507, 702, 1014, 1521, 3042, 4563, 9126
The HCF of 2409,9126 is 3.
Lets's calculate GCF of 2409,9126
| 3 | 2409, 9126 |
| 803, 3042 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2409,9126 By Matching Biggest Common Factor Method
Now, list down the factors of 2409
:1,3,11,33,73,219,803,2409
Now, list down the factors of 9126
:1,2,3,6,9,13,18,26,27,39,54,78,117,169,234,338,351,507,702,1014,1521,3042,4563,9126
Greatest Common Factor
We found the factors 2409,9126 . The biggest common factor number is the GCF number.
So the greatest common factor 2409,9126 is 3.
Lets's calculate LCM of 144,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 60336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/60336
Therefore, the GCF of Fractions 2409/144,9126/419 is 3/60336
Least Common Multiple of 144,419 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 144,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(144,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(144,419) x common factors =1 x 1 = 1
LCM(144,419) = ( 144 × 419 ) / 1
LCM(144,419) = 60336 / 1
LCM(144,419) = 60336
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FAQs on GCF of Fractions of 2409/144, 9126/419
1. What is the HCF of 2409,9126?
The HCF of 2409,9126 is 3
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 2409/144, 9126/419?
Answer: GCF of Numerators as per given numbers 2409/144, 9126/419 is
GCF of Numerators i.e. for 2409,9126 is 3
LCM of denominators i.e. for 144,419 is 60336.
Thus, GCF of Fractions is 3/60336.Finally, GCF of Fractions for 2409/144, 9126/419 is 3/60336.