Use our free GCF of Fractions Calculator tool to compute the GCF of 305/564, 675/430 i.e 5/121260 easily. The following is the detailed procedure to determine the greatest common factor of fractions 305/564, 675/430.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 305/564,675/430
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 305/564,675/430, numerators are 305,675
Denominators are 564,430
The GCF of 305,675 is 5 .
LCM of 564,430 is 121260.
The greatest common factor of 305/564,675/430 = [GCF of 305,675]/[LCM of 564,430]= 5/121260
Therefore, the GCF of 305/564,675/430 is 5/121260.
To find the highest common factor of 305,675, we have to find the factors of both numbers and list the highest common factor.
The factors of 305 are 1, 5, 61, 305
The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
The HCF of 305,675 is 5.
Lets's calculate GCF of 305,675
5 | 305, 675 |
61, 135 |
∴ So the GCF of the given numbers is 5 = 5
Now, list down the factors of 305
:1,5,61,305
Now, list down the factors of 675
:1,3,5,9,15,25,27,45,75,135,225,675
Greatest Common Factor
We found the factors 305,675 . The biggest common factor number is the GCF number.
So the greatest common factor 305,675 is 5.
Lets's calculate LCM of 564,430
2 | 564, 430 |
282, 215 |
∴ So the LCM of the given numbers is 2 x 282 x 215 = 121260
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/121260
Therefore, the GCF of Fractions 305/564,675/430 is 5/121260
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 564,430 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(564,430) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(564,430) x common factors =2 x 1 = 2
LCM(564,430) = ( 564 × 430 ) / 2
LCM(564,430) = 242520 / 2
LCM(564,430) = 121260
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 305,675?
The HCF of 305,675 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 305/564, 675/430?
Answer: GCF of Numerators as per given numbers 305/564, 675/430 is
GCF of Numerators i.e. for 305,675 is 5
LCM of denominators i.e. for 564,430 is 121260.
Thus, GCF of Fractions is 5/121260.Finally, GCF of Fractions for 305/564, 675/430 is 5/121260.