Use our free GCF of Fractions Calculator tool to compute the GCF of 318/412, 518/909 i.e 2/374508 easily. The following is the detailed procedure to determine the greatest common factor of fractions 318/412, 518/909.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 318/412,518/909
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 318/412,518/909, numerators are 318,518
Denominators are 412,909
The GCF of 318,518 is 2 .
LCM of 412,909 is 374508.
The greatest common factor of 318/412,518/909 = [GCF of 318,518]/[LCM of 412,909]= 2/374508
Therefore, the GCF of 318/412,518/909 is 2/374508.
To find the highest common factor of 318,518, we have to find the factors of both numbers and list the highest common factor.
The factors of 318 are 1, 2, 3, 6, 53, 106, 159, 318
The factors of 518 are 1, 2, 7, 14, 37, 74, 259, 518
The HCF of 318,518 is 2.
Lets's calculate GCF of 318,518
2 | 318, 518 |
159, 259 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 318
:1,2,3,6,53,106,159,318
Now, list down the factors of 518
:1,2,7,14,37,74,259,518
Greatest Common Factor
We found the factors 318,518 . The biggest common factor number is the GCF number.
So the greatest common factor 318,518 is 2.
Lets's calculate LCM of 412,909
Given numbers has no common factors except 1. So, there LCM is their product i.e 374508
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/374508
Therefore, the GCF of Fractions 318/412,518/909 is 2/374508
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 412,909 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(412,909) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(412,909) x common factors =1 x 1 = 1
LCM(412,909) = ( 412 × 909 ) / 1
LCM(412,909) = 374508 / 1
LCM(412,909) = 374508
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 318,518?
The HCF of 318,518 is 2
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 318/412, 518/909?
Answer: GCF of Numerators as per given numbers 318/412, 518/909 is
GCF of Numerators i.e. for 318,518 is 2
LCM of denominators i.e. for 412,909 is 374508.
Thus, GCF of Fractions is 2/374508.Finally, GCF of Fractions for 318/412, 518/909 is 2/374508.