Use our free GCF of Fractions Calculator tool to compute the GCF of 612/116, 636/309 i.e 12/35844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 612/116, 636/309.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 612/116,636/309
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 612/116,636/309, numerators are 612,636
Denominators are 116,309
The GCF of 612,636 is 12 .
LCM of 116,309 is 35844.
The greatest common factor of 612/116,636/309 = [GCF of 612,636]/[LCM of 116,309]= 12/35844
Therefore, the GCF of 612/116,636/309 is 12/35844.
To find the highest common factor of 612,636, we have to find the factors of both numbers and list the highest common factor.
The factors of 612 are 1, 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204, 306, 612
The factors of 636 are 1, 2, 3, 4, 6, 12, 53, 106, 159, 212, 318, 636
The HCF of 612,636 is 12.
Lets's calculate GCF of 612,636
2 | 612, 636 |
2 | 306, 318 |
3 | 153, 159 |
51, 53 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 612
:1,2,3,4,6,9,12,17,18,34,36,51,68,102,153,204,306,612
Now, list down the factors of 636
:1,2,3,4,6,12,53,106,159,212,318,636
Greatest Common Factor
We found the factors 612,636 . The biggest common factor number is the GCF number.
So the greatest common factor 612,636 is 12.
Lets's calculate LCM of 116,309
Given numbers has no common factors except 1. So, there LCM is their product i.e 35844
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/35844
Therefore, the GCF of Fractions 612/116,636/309 is 12/35844
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 116,309 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(116,309) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(116,309) x common factors =1 x 1 = 1
LCM(116,309) = ( 116 × 309 ) / 1
LCM(116,309) = 35844 / 1
LCM(116,309) = 35844
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 612,636?
The HCF of 612,636 is 12
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 612/116, 636/309?
Answer: GCF of Numerators as per given numbers 612/116, 636/309 is
GCF of Numerators i.e. for 612,636 is 12
LCM of denominators i.e. for 116,309 is 35844.
Thus, GCF of Fractions is 12/35844.Finally, GCF of Fractions for 612/116, 636/309 is 12/35844.