Use our free GCF of Fractions Calculator tool to compute the GCF of 417/254, 758/610 i.e 1/77470 easily. The following is the detailed procedure to determine the greatest common factor of fractions 417/254, 758/610.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 417/254,758/610
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 417/254,758/610, numerators are 417,758
Denominators are 254,610
The GCF of 417,758 is 1 .
LCM of 254,610 is 77470.
The greatest common factor of 417/254,758/610 = [GCF of 417,758]/[LCM of 254,610]= 1/77470
Therefore, the GCF of 417/254,758/610 is 1/77470.
To find the highest common factor of 417,758, we have to find the factors of both numbers and list the highest common factor.
The factors of 417 are 1, 3, 139, 417
The factors of 758 are 1, 2, 379, 758
The HCF of 417,758 is 1.
Lets's calculate GCF of 417,758
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 417
:1,3,139,417
Now, list down the factors of 758
:1,2,379,758
Greatest Common Factor
We found the factors 417,758 . The biggest common factor number is the GCF number.
So the greatest common factor 417,758 is 1.
Lets's calculate LCM of 254,610
2 | 254, 610 |
127, 305 |
∴ So the LCM of the given numbers is 2 x 127 x 305 = 77470
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/77470
Therefore, the GCF of Fractions 417/254,758/610 is 1/77470
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 254,610 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(254,610) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(254,610) x common factors =2 x 1 = 2
LCM(254,610) = ( 254 × 610 ) / 2
LCM(254,610) = 154940 / 2
LCM(254,610) = 77470
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 417,758?
The HCF of 417,758 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 417/254, 758/610?
Answer: GCF of Numerators as per given numbers 417/254, 758/610 is
GCF of Numerators i.e. for 417,758 is 1
LCM of denominators i.e. for 254,610 is 77470.
Thus, GCF of Fractions is 1/77470.Finally, GCF of Fractions for 417/254, 758/610 is 1/77470.