GCF of 6565/114, 6734/192
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6565/114, 6734/192 i.e 13/3648 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6565/114, 6734/192.
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 6565/114,6734/192?
Given fractions are 6565/114,6734/192
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 6565/114,6734/192, numerators are 6565,6734
Denominators are 114,192
The GCF of 6565,6734 is 13 .
LCM of 114,192 is 3648.
The greatest common factor of 6565/114,6734/192 = [GCF of 6565,6734]/[LCM of 114,192]= 13/3648
Therefore, the GCF of 6565/114,6734/192 is 13/3648.
To find the highest common factor of 6565,6734, we have to find the factors of both numbers and list the highest common factor.
The factors of 6565 are 1, 5, 13, 65, 101, 505, 1313, 6565
The factors of 6734 are 1, 2, 7, 13, 14, 26, 37, 74, 91, 182, 259, 481, 518, 962, 3367, 6734
The HCF of 6565,6734 is 13.
Lets's calculate GCF of 6565,6734
| 13 | 6565, 6734 |
| 505, 518 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 6565,6734 By Matching Biggest Common Factor Method
Now, list down the factors of 6565
:1,5,13,65,101,505,1313,6565
Now, list down the factors of 6734
:1,2,7,13,14,26,37,74,91,182,259,481,518,962,3367,6734
Greatest Common Factor
We found the factors 6565,6734 . The biggest common factor number is the GCF number.
So the greatest common factor 6565,6734 is 13.
Lets's calculate LCM of 114,192
| 2 | 114, 192 |
| 3 | 57, 96 |
| 19, 32 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 32 = 3648
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/3648
Therefore, the GCF of Fractions 6565/114,6734/192 is 13/3648
Least Common Multiple of 114,192 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 114,192 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(114,192) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(114,192) x common factors =6 x 1 = 6
LCM(114,192) = ( 114 × 192 ) / 6
LCM(114,192) = 21888 / 6
LCM(114,192) = 3648
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FAQs on GCF of Fractions of 6565/114, 6734/192
1. What is the HCF of 6565,6734?
The HCF of 6565,6734 is 13
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 6565/114, 6734/192?
Answer: GCF of Numerators as per given numbers 6565/114, 6734/192 is
GCF of Numerators i.e. for 6565,6734 is 13
LCM of denominators i.e. for 114,192 is 3648.
Thus, GCF of Fractions is 13/3648.Finally, GCF of Fractions for 6565/114, 6734/192 is 13/3648.