Use our free GCF of Fractions Calculator tool to compute the GCF of 415/97, 680/8129 i.e 5/788513 easily. The following is the detailed procedure to determine the greatest common factor of fractions 415/97, 680/8129.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 415/97,680/8129
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 415/97,680/8129, numerators are 415,680
Denominators are 97,8129
The GCF of 415,680 is 5 .
LCM of 97,8129 is 788513.
The greatest common factor of 415/97,680/8129 = [GCF of 415,680]/[LCM of 97,8129]= 5/788513
Therefore, the GCF of 415/97,680/8129 is 5/788513.
To find the highest common factor of 415,680, we have to find the factors of both numbers and list the highest common factor.
The factors of 415 are 1, 5, 83, 415
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The HCF of 415,680 is 5.
Lets's calculate GCF of 415,680
5 | 415, 680 |
83, 136 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 415
:1,5,83,415
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Greatest Common Factor
We found the factors 415,680 . The biggest common factor number is the GCF number.
So the greatest common factor 415,680 is 5.
Lets's calculate LCM of 97,8129
Given numbers has no common factors except 1. So, there LCM is their product i.e 788513
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/788513
Therefore, the GCF of Fractions 415/97,680/8129 is 5/788513
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 97,8129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(97,8129) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(97,8129) x common factors =1 x 1 = 1
LCM(97,8129) = ( 97 × 8129 ) / 1
LCM(97,8129) = 788513 / 1
LCM(97,8129) = 788513
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 415,680?
The HCF of 415,680 is 5
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 415/97, 680/8129?
Answer: GCF of Numerators as per given numbers 415/97, 680/8129 is
GCF of Numerators i.e. for 415,680 is 5
LCM of denominators i.e. for 97,8129 is 788513.
Thus, GCF of Fractions is 5/788513.Finally, GCF of Fractions for 415/97, 680/8129 is 5/788513.