Use our free GCF of Fractions Calculator tool to compute the GCF of 488/432, 305/548 i.e 61/59184 easily. The following is the detailed procedure to determine the greatest common factor of fractions 488/432, 305/548.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 488/432,305/548
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 488/432,305/548, numerators are 488,305
Denominators are 432,548
The GCF of 488,305 is 61 .
LCM of 432,548 is 59184.
The greatest common factor of 488/432,305/548 = [GCF of 488,305]/[LCM of 432,548]= 61/59184
Therefore, the GCF of 488/432,305/548 is 61/59184.
To find the highest common factor of 488,305, we have to find the factors of both numbers and list the highest common factor.
The factors of 488 are 1, 2, 4, 8, 61, 122, 244, 488
The factors of 305 are 1, 5, 61, 305
The HCF of 488,305 is 61.
Lets's calculate GCF of 488,305
61 | 488, 305 |
8, 5 |
∴ So the GCF of the given numbers is 61 = 61
Now, list down the factors of 488
:1,2,4,8,61,122,244,488
Now, list down the factors of 305
:1,5,61,305
Greatest Common Factor
We found the factors 488,305 . The biggest common factor number is the GCF number.
So the greatest common factor 488,305 is 61.
Lets's calculate LCM of 432,548
2 | 432, 548 |
2 | 216, 274 |
108, 137 |
∴ So the LCM of the given numbers is 2 x 2 x 108 x 137 = 59184
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 61/59184
Therefore, the GCF of Fractions 488/432,305/548 is 61/59184
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 432,548 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(432,548) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(432,548) x common factors =4 x 1 = 4
LCM(432,548) = ( 432 × 548 ) / 4
LCM(432,548) = 236736 / 4
LCM(432,548) = 59184
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 488,305?
The HCF of 488,305 is 61
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 488/432, 305/548?
Answer: GCF of Numerators as per given numbers 488/432, 305/548 is
GCF of Numerators i.e. for 488,305 is 61
LCM of denominators i.e. for 432,548 is 59184.
Thus, GCF of Fractions is 61/59184.Finally, GCF of Fractions for 488/432, 305/548 is 61/59184.