Use our free GCF of Fractions Calculator tool to compute the GCF of 105/828, 760/541 i.e 5/447948 easily. The following is the detailed procedure to determine the greatest common factor of fractions 105/828, 760/541.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 105/828,760/541
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 105/828,760/541, numerators are 105,760
Denominators are 828,541
The GCF of 105,760 is 5 .
LCM of 828,541 is 447948.
The greatest common factor of 105/828,760/541 = [GCF of 105,760]/[LCM of 828,541]= 5/447948
Therefore, the GCF of 105/828,760/541 is 5/447948.
To find the highest common factor of 105,760, we have to find the factors of both numbers and list the highest common factor.
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The HCF of 105,760 is 5.
Lets's calculate GCF of 105,760
5 | 105, 760 |
21, 152 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Now, list down the factors of 760
:1,2,4,5,8,10,19,20,38,40,76,95,152,190,380,760
Greatest Common Factor
We found the factors 105,760 . The biggest common factor number is the GCF number.
So the greatest common factor 105,760 is 5.
Lets's calculate LCM of 828,541
Given numbers has no common factors except 1. So, there LCM is their product i.e 447948
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/447948
Therefore, the GCF of Fractions 105/828,760/541 is 5/447948
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 828,541 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(828,541) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(828,541) x common factors =1 x 1 = 1
LCM(828,541) = ( 828 × 541 ) / 1
LCM(828,541) = 447948 / 1
LCM(828,541) = 447948
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 105,760?
The HCF of 105,760 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 105/828, 760/541?
Answer: GCF of Numerators as per given numbers 105/828, 760/541 is
GCF of Numerators i.e. for 105,760 is 5
LCM of denominators i.e. for 828,541 is 447948.
Thus, GCF of Fractions is 5/447948.Finally, GCF of Fractions for 105/828, 760/541 is 5/447948.