GCF of 728/208, 8575/646
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 728/208, 8575/646 i.e 7/67184 easily. The following is the detailed procedure to determine the greatest common factor of fractions 728/208, 8575/646.
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 728/208,8575/646?
Given fractions are 728/208,8575/646
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 728/208,8575/646, numerators are 728,8575
Denominators are 208,646
The GCF of 728,8575 is 7 .
LCM of 208,646 is 67184.
The greatest common factor of 728/208,8575/646 = [GCF of 728,8575]/[LCM of 208,646]= 7/67184
Therefore, the GCF of 728/208,8575/646 is 7/67184.
To find the highest common factor of 728,8575, we have to find the factors of both numbers and list the highest common factor.
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The factors of 8575 are 1, 5, 7, 25, 35, 49, 175, 245, 343, 1225, 1715, 8575
The HCF of 728,8575 is 7.
Lets's calculate GCF of 728,8575
| 7 | 728, 8575 |
| 104, 1225 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 728,8575 By Matching Biggest Common Factor Method
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Now, list down the factors of 8575
:1,5,7,25,35,49,175,245,343,1225,1715,8575
Greatest Common Factor
We found the factors 728,8575 . The biggest common factor number is the GCF number.
So the greatest common factor 728,8575 is 7.
Lets's calculate LCM of 208,646
| 2 | 208, 646 |
| 104, 323 |
∴ So the LCM of the given numbers is 2 x 104 x 323 = 67184
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/67184
Therefore, the GCF of Fractions 728/208,8575/646 is 7/67184
Least Common Multiple of 208,646 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 208,646 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,646) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(208,646) x common factors =2 x 1 = 2
LCM(208,646) = ( 208 × 646 ) / 2
LCM(208,646) = 134368 / 2
LCM(208,646) = 67184
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FAQs on GCF of Fractions of 728/208, 8575/646
1. What is the HCF of 728,8575?
The HCF of 728,8575 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 728/208, 8575/646?
Answer: GCF of Numerators as per given numbers 728/208, 8575/646 is
GCF of Numerators i.e. for 728,8575 is 7
LCM of denominators i.e. for 208,646 is 67184.
Thus, GCF of Fractions is 7/67184.Finally, GCF of Fractions for 728/208, 8575/646 is 7/67184.