Use our free GCF of Fractions Calculator tool to compute the GCF of 108/416, 385/825 i.e 1/343200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 108/416, 385/825.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 108/416,385/825
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 108/416,385/825, numerators are 108,385
Denominators are 416,825
The GCF of 108,385 is 1 .
LCM of 416,825 is 343200.
The greatest common factor of 108/416,385/825 = [GCF of 108,385]/[LCM of 416,825]= 1/343200
Therefore, the GCF of 108/416,385/825 is 1/343200.
To find the highest common factor of 108,385, we have to find the factors of both numbers and list the highest common factor.
The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
The factors of 385 are 1, 5, 7, 11, 35, 55, 77, 385
The HCF of 108,385 is 1.
Lets's calculate GCF of 108,385
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 108
:1,2,3,4,6,9,12,18,27,36,54,108
Now, list down the factors of 385
:1,5,7,11,35,55,77,385
Greatest Common Factor
We found the factors 108,385 . The biggest common factor number is the GCF number.
So the greatest common factor 108,385 is 1.
Lets's calculate LCM of 416,825
Given numbers has no common factors except 1. So, there LCM is their product i.e 343200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/343200
Therefore, the GCF of Fractions 108/416,385/825 is 1/343200
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 416,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(416,825) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(416,825) x common factors =1 x 1 = 1
LCM(416,825) = ( 416 × 825 ) / 1
LCM(416,825) = 343200 / 1
LCM(416,825) = 343200
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 108,385?
The HCF of 108,385 is 1
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 108/416, 385/825?
Answer: GCF of Numerators as per given numbers 108/416, 385/825 is
GCF of Numerators i.e. for 108,385 is 1
LCM of denominators i.e. for 416,825 is 343200.
Thus, GCF of Fractions is 1/343200.Finally, GCF of Fractions for 108/416, 385/825 is 1/343200.