GCF of 806/30, 325/256
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 806/30, 325/256 i.e 13/3840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 806/30, 325/256.
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 806/30,325/256?
Given fractions are 806/30,325/256
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 806/30,325/256, numerators are 806,325
Denominators are 30,256
The GCF of 806,325 is 13 .
LCM of 30,256 is 3840.
The greatest common factor of 806/30,325/256 = [GCF of 806,325]/[LCM of 30,256]= 13/3840
Therefore, the GCF of 806/30,325/256 is 13/3840.
To find the highest common factor of 806,325, we have to find the factors of both numbers and list the highest common factor.
The factors of 806 are 1, 2, 13, 26, 31, 62, 403, 806
The factors of 325 are 1, 5, 13, 25, 65, 325
The HCF of 806,325 is 13.
Lets's calculate GCF of 806,325
| 13 | 806, 325 |
| 62, 25 |
∴ So the GCF of the given numbers is 13 = 13
Greatest Common Factor of 806,325 By Matching Biggest Common Factor Method
Now, list down the factors of 806
:1,2,13,26,31,62,403,806
Now, list down the factors of 325
:1,5,13,25,65,325
Greatest Common Factor
We found the factors 806,325 . The biggest common factor number is the GCF number.
So the greatest common factor 806,325 is 13.
Lets's calculate LCM of 30,256
| 2 | 30, 256 |
| 15, 128 |
∴ So the LCM of the given numbers is 2 x 15 x 128 = 3840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/3840
Therefore, the GCF of Fractions 806/30,325/256 is 13/3840
Least Common Multiple of 30,256 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 30,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,256) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(30,256) x common factors =2 x 1 = 2
LCM(30,256) = ( 30 × 256 ) / 2
LCM(30,256) = 7680 / 2
LCM(30,256) = 3840
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FAQs on GCF of Fractions of 806/30, 325/256
1. What is the HCF of 806,325?
The HCF of 806,325 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 806/30, 325/256?
Answer: GCF of Numerators as per given numbers 806/30, 325/256 is
GCF of Numerators i.e. for 806,325 is 13
LCM of denominators i.e. for 30,256 is 3840.
Thus, GCF of Fractions is 13/3840.Finally, GCF of Fractions for 806/30, 325/256 is 13/3840.