Use our free GCF of Fractions Calculator tool to compute the GCF of 805/316, 728/920 i.e 7/72680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 805/316, 728/920.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 805/316,728/920
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 805/316,728/920, numerators are 805,728
Denominators are 316,920
The GCF of 805,728 is 7 .
LCM of 316,920 is 72680.
The greatest common factor of 805/316,728/920 = [GCF of 805,728]/[LCM of 316,920]= 7/72680
Therefore, the GCF of 805/316,728/920 is 7/72680.
To find the highest common factor of 805,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 805 are 1, 5, 7, 23, 35, 115, 161, 805
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 805,728 is 7.
Lets's calculate GCF of 805,728
7 | 805, 728 |
115, 104 |
∴ So the GCF of the given numbers is 7 = 7
Now, list down the factors of 805
:1,5,7,23,35,115,161,805
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 805,728 . The biggest common factor number is the GCF number.
So the greatest common factor 805,728 is 7.
Lets's calculate LCM of 316,920
2 | 316, 920 |
2 | 158, 460 |
79, 230 |
∴ So the LCM of the given numbers is 2 x 2 x 79 x 230 = 72680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/72680
Therefore, the GCF of Fractions 805/316,728/920 is 7/72680
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 316,920 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(316,920) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(316,920) x common factors =4 x 1 = 4
LCM(316,920) = ( 316 × 920 ) / 4
LCM(316,920) = 290720 / 4
LCM(316,920) = 72680
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 805,728?
The HCF of 805,728 is 7
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 805/316, 728/920?
Answer: GCF of Numerators as per given numbers 805/316, 728/920 is
GCF of Numerators i.e. for 805,728 is 7
LCM of denominators i.e. for 316,920 is 72680.
Thus, GCF of Fractions is 7/72680.Finally, GCF of Fractions for 805/316, 728/920 is 7/72680.