Use our free GCF of Fractions Calculator tool to compute the GCF of 415/46, 806/54, 752/72 i.e 1/4968 easily. The following is the detailed procedure to determine the greatest common factor of fractions 415/46, 806/54, 752/72.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 415/46,806/54,752/72
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 415/46,806/54,752/72, numerators are 415,806,752
Denominators are 46,54,72
The GCF of 415,806,752 is 1 .
LCM of 46,54,72 is 4968.
The greatest common factor of 415/46,806/54,752/72 = [GCF of 415,806,752]/[LCM of 46,54,72]= 1/4968
Therefore, the GCF of 415/46,806/54,752/72 is 1/4968.
To find the highest common factor of 415,806,752, we have to find the factors of both numbers and list the highest common factor.
The factors of 415 are 1, 5, 83, 415
The factors of 806 are 1, 2, 13, 26, 31, 62, 403, 806
The factors of 752 are 1, 2, 4, 8, 16, 47, 94, 188, 376, 752
The HCF of 415,806,752 is 1.
Lets's calculate GCF of 415,806,752
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 415
:1,5,83,415
Now, list down the factors of 806
:1,2,13,26,31,62,403,806
Now, list down the factors of 752
:1,2,4,8,16,47,94,188,376,752
Greatest Common Factor
We found the factors 415,806,752 . The biggest common factor number is the GCF number.
So the greatest common factor 415,806,752 is 1.
Lets's calculate LCM of 46,54,72
2 | 46, 54, 72 |
3 | 23, 27, 36 |
3 | 23, 9, 12 |
23, 3, 4 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 23 x 3 x 4 = 4968
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/4968
Therefore, the GCF of Fractions 415/46,806/54,752/72 is 1/4968
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 46,54,72 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(46,54,72) = 2
common factors(in case of two or more numbers have common factors) = 18
GCF(46,54,72) x common factors =2 x 18 = 36
LCM(46,54,72) = ( 46 × 54 × 72 ) / 36
LCM(46,54,72) = 178848 / 36
LCM(46,54,72) = 4968
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 415,806,752?
The HCF of 415,806,752 is 1
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 415/46, 806/54, 752/72?
Answer: GCF of Numerators as per given numbers 415/46, 806/54, 752/72 is
GCF of Numerators i.e. for 415,806,752 is 1
LCM of denominators i.e. for 46,54,72 is 4968.
Thus, GCF of Fractions is 1/4968.Finally, GCF of Fractions for 415/46, 806/54, 752/72 is 1/4968.