Use our free GCF of Fractions Calculator tool to compute the GCF of 310/123, 609/101 i.e 1/12423 easily. The following is the detailed procedure to determine the greatest common factor of fractions 310/123, 609/101.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 310/123,609/101
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 310/123,609/101, numerators are 310,609
Denominators are 123,101
The GCF of 310,609 is 1 .
LCM of 123,101 is 12423.
The greatest common factor of 310/123,609/101 = [GCF of 310,609]/[LCM of 123,101]= 1/12423
Therefore, the GCF of 310/123,609/101 is 1/12423.
To find the highest common factor of 310,609, we have to find the factors of both numbers and list the highest common factor.
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The HCF of 310,609 is 1.
Lets's calculate GCF of 310,609
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Greatest Common Factor
We found the factors 310,609 . The biggest common factor number is the GCF number.
So the greatest common factor 310,609 is 1.
Lets's calculate LCM of 123,101
Given numbers has no common factors except 1. So, there LCM is their product i.e 12423
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12423
Therefore, the GCF of Fractions 310/123,609/101 is 1/12423
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 123,101 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(123,101) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(123,101) x common factors =1 x 1 = 1
LCM(123,101) = ( 123 × 101 ) / 1
LCM(123,101) = 12423 / 1
LCM(123,101) = 12423
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 310,609?
The HCF of 310,609 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 310/123, 609/101?
Answer: GCF of Numerators as per given numbers 310/123, 609/101 is
GCF of Numerators i.e. for 310,609 is 1
LCM of denominators i.e. for 123,101 is 12423.
Thus, GCF of Fractions is 1/12423.Finally, GCF of Fractions for 310/123, 609/101 is 1/12423.