Use our free GCF of Fractions Calculator tool to compute the GCF of 316/857, 760/225 i.e 4/192825 easily. The following is the detailed procedure to determine the greatest common factor of fractions 316/857, 760/225.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 316/857,760/225
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 316/857,760/225, numerators are 316,760
Denominators are 857,225
The GCF of 316,760 is 4 .
LCM of 857,225 is 192825.
The greatest common factor of 316/857,760/225 = [GCF of 316,760]/[LCM of 857,225]= 4/192825
Therefore, the GCF of 316/857,760/225 is 4/192825.
To find the highest common factor of 316,760, we have to find the factors of both numbers and list the highest common factor.
The factors of 316 are 1, 2, 4, 79, 158, 316
The factors of 760 are 1, 2, 4, 5, 8, 10, 19, 20, 38, 40, 76, 95, 152, 190, 380, 760
The HCF of 316,760 is 4.
Lets's calculate GCF of 316,760
2 | 316, 760 |
2 | 158, 380 |
79, 190 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 316
:1,2,4,79,158,316
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 316,760 . The biggest common factor number is the GCF number.
So the greatest common factor 316,760 is 4.
Lets's calculate LCM of 857,225
Given numbers has no common factors except 1. So, there LCM is their product i.e 192825
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/192825
Therefore, the GCF of Fractions 316/857,760/225 is 4/192825
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 857,225 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(857,225) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(857,225) x common factors =1 x 1 = 1
LCM(857,225) = ( 857 × 225 ) / 1
LCM(857,225) = 192825 / 1
LCM(857,225) = 192825
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 316,760?
The HCF of 316,760 is 4
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 316/857, 760/225?
Answer: GCF of Numerators as per given numbers 316/857, 760/225 is
GCF of Numerators i.e. for 316,760 is 4
LCM of denominators i.e. for 857,225 is 192825.
Thus, GCF of Fractions is 4/192825.Finally, GCF of Fractions for 316/857, 760/225 is 4/192825.