Use our free GCF of Fractions Calculator tool to compute the GCF of 585/812, 725/280 i.e 5/8120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 585/812, 725/280.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 585/812,725/280
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 585/812,725/280, numerators are 585,725
Denominators are 812,280
The GCF of 585,725 is 5 .
LCM of 812,280 is 8120.
The greatest common factor of 585/812,725/280 = [GCF of 585,725]/[LCM of 812,280]= 5/8120
Therefore, the GCF of 585/812,725/280 is 5/8120.
To find the highest common factor of 585,725, we have to find the factors of both numbers and list the highest common factor.
The factors of 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
The factors of 725 are 1, 5, 25, 29, 145, 725
The HCF of 585,725 is 5.
Lets's calculate GCF of 585,725
5 | 585, 725 |
117, 145 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 585
:1,3,5,9,13,15,39,45,65,117,195,585
Now, list down the factors of 725
:1,5,25,29,145,725
Greatest Common Factor
We found the factors 585,725 . The biggest common factor number is the GCF number.
So the greatest common factor 585,725 is 5.
Lets's calculate LCM of 812,280
2 | 812, 280 |
2 | 406, 140 |
7 | 203, 70 |
29, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 29 x 10 = 8120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/8120
Therefore, the GCF of Fractions 585/812,725/280 is 5/8120
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 812,280 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(812,280) = 28
common factors(in case of two or more numbers have common factors) = 1
GCF(812,280) x common factors =28 x 1 = 28
LCM(812,280) = ( 812 × 280 ) / 28
LCM(812,280) = 227360 / 28
LCM(812,280) = 8120
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 585,725?
The HCF of 585,725 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 585/812, 725/280?
Answer: GCF of Numerators as per given numbers 585/812, 725/280 is
GCF of Numerators i.e. for 585,725 is 5
LCM of denominators i.e. for 812,280 is 8120.
Thus, GCF of Fractions is 5/8120.Finally, GCF of Fractions for 585/812, 725/280 is 5/8120.