Use our free GCF of Fractions Calculator tool to compute the GCF of 6975/171, 9835/9747 i.e 5/9747 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6975/171, 9835/9747.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 6975/171,9835/9747
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 6975/171,9835/9747, numerators are 6975,9835
Denominators are 171,9747
The GCF of 6975,9835 is 5 .
LCM of 171,9747 is 9747.
The greatest common factor of 6975/171,9835/9747 = [GCF of 6975,9835]/[LCM of 171,9747]= 5/9747
Therefore, the GCF of 6975/171,9835/9747 is 5/9747.
To find the highest common factor of 6975,9835, we have to find the factors of both numbers and list the highest common factor.
The factors of 6975 are 1, 3, 5, 9, 15, 25, 31, 45, 75, 93, 155, 225, 279, 465, 775, 1395, 2325, 6975
The factors of 9835 are 1, 5, 7, 35, 281, 1405, 1967, 9835
The HCF of 6975,9835 is 5.
Lets's calculate GCF of 6975,9835
5 | 6975, 9835 |
1395, 1967 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 6975
:1,3,5,9,15,25,31,45,75,93,155,225,279,465,775,1395,2325,6975
Now, list down the factors of 9835
:1,5,7,35,281,1405,1967,9835
Greatest Common Factor
We found the factors 6975,9835 . The biggest common factor number is the GCF number.
So the greatest common factor 6975,9835 is 5.
Lets's calculate LCM of 171,9747
3 | 171, 9747 |
3 | 57, 3249 |
19 | 19, 1083 |
1, 57 |
∴ So the LCM of the given numbers is 3 x 3 x 19 x 1 x 57 = 9747
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/9747
Therefore, the GCF of Fractions 6975/171,9835/9747 is 5/9747
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 171,9747 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(171,9747) = 171
common factors(in case of two or more numbers have common factors) = 1
GCF(171,9747) x common factors =171 x 1 = 171
LCM(171,9747) = ( 171 × 9747 ) / 171
LCM(171,9747) = 1666737 / 171
LCM(171,9747) = 9747
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 6975,9835?
The HCF of 6975,9835 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 6975/171, 9835/9747?
Answer: GCF of Numerators as per given numbers 6975/171, 9835/9747 is
GCF of Numerators i.e. for 6975,9835 is 5
LCM of denominators i.e. for 171,9747 is 9747.
Thus, GCF of Fractions is 5/9747.Finally, GCF of Fractions for 6975/171, 9835/9747 is 5/9747.