GCF of 649/102, 8349/289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 649/102, 8349/289 i.e 11/1734 easily. The following is the detailed procedure to determine the greatest common factor of fractions 649/102, 8349/289.
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 649/102,8349/289?
Given fractions are 649/102,8349/289
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 649/102,8349/289, numerators are 649,8349
Denominators are 102,289
The GCF of 649,8349 is 11 .
LCM of 102,289 is 1734.
The greatest common factor of 649/102,8349/289 = [GCF of 649,8349]/[LCM of 102,289]= 11/1734
Therefore, the GCF of 649/102,8349/289 is 11/1734.
To find the highest common factor of 649,8349, we have to find the factors of both numbers and list the highest common factor.
The factors of 649 are 1, 11, 59, 649
The factors of 8349 are 1, 3, 11, 23, 33, 69, 121, 253, 363, 759, 2783, 8349
The HCF of 649,8349 is 11.
Lets's calculate GCF of 649,8349
| 11 | 649, 8349 |
| 59, 759 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 649,8349 By Matching Biggest Common Factor Method
Now, list down the factors of 649
:1,11,59,649
Now, list down the factors of 8349
:1,3,11,23,33,69,121,253,363,759,2783,8349
Greatest Common Factor
We found the factors 649,8349 . The biggest common factor number is the GCF number.
So the greatest common factor 649,8349 is 11.
Lets's calculate LCM of 102,289
| 17 | 102, 289 |
| 6, 17 |
∴ So the LCM of the given numbers is 17 x 6 x 17 = 1734
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/1734
Therefore, the GCF of Fractions 649/102,8349/289 is 11/1734
Least Common Multiple of 102,289 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 102,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(102,289) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(102,289) x common factors =17 x 1 = 17
LCM(102,289) = ( 102 × 289 ) / 17
LCM(102,289) = 29478 / 17
LCM(102,289) = 1734
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FAQs on GCF of Fractions of 649/102, 8349/289
1. What is the HCF of 649,8349?
The HCF of 649,8349 is 11
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 649/102, 8349/289?
Answer: GCF of Numerators as per given numbers 649/102, 8349/289 is
GCF of Numerators i.e. for 649,8349 is 11
LCM of denominators i.e. for 102,289 is 1734.
Thus, GCF of Fractions is 11/1734.Finally, GCF of Fractions for 649/102, 8349/289 is 11/1734.