GCF of 2569/264, 5509/649
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2569/264, 5509/649 i.e 7/15576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2569/264, 5509/649.
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 2569/264,5509/649?
Given fractions are 2569/264,5509/649
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 2569/264,5509/649, numerators are 2569,5509
Denominators are 264,649
The GCF of 2569,5509 is 7 .
LCM of 264,649 is 15576.
The greatest common factor of 2569/264,5509/649 = [GCF of 2569,5509]/[LCM of 264,649]= 7/15576
Therefore, the GCF of 2569/264,5509/649 is 7/15576.
To find the highest common factor of 2569,5509, we have to find the factors of both numbers and list the highest common factor.
The factors of 2569 are 1, 7, 367, 2569
The factors of 5509 are 1, 7, 787, 5509
The HCF of 2569,5509 is 7.
Lets's calculate GCF of 2569,5509
| 7 | 2569, 5509 |
| 367, 787 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 2569,5509 By Matching Biggest Common Factor Method
Now, list down the factors of 2569
:1,7,367,2569
Now, list down the factors of 5509
:1,7,787,5509
Greatest Common Factor
We found the factors 2569,5509 . The biggest common factor number is the GCF number.
So the greatest common factor 2569,5509 is 7.
Lets's calculate LCM of 264,649
| 11 | 264, 649 |
| 24, 59 |
∴ So the LCM of the given numbers is 11 x 24 x 59 = 15576
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/15576
Therefore, the GCF of Fractions 2569/264,5509/649 is 7/15576
Least Common Multiple of 264,649 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 264,649 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(264,649) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(264,649) x common factors =11 x 1 = 11
LCM(264,649) = ( 264 × 649 ) / 11
LCM(264,649) = 171336 / 11
LCM(264,649) = 15576
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FAQs on GCF of Fractions of 2569/264, 5509/649
1. What is the HCF of 2569,5509?
The HCF of 2569,5509 is 7
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 2569/264, 5509/649?
Answer: GCF of Numerators as per given numbers 2569/264, 5509/649 is
GCF of Numerators i.e. for 2569,5509 is 7
LCM of denominators i.e. for 264,649 is 15576.
Thus, GCF of Fractions is 7/15576.Finally, GCF of Fractions for 2569/264, 5509/649 is 7/15576.