Use our free GCF of Fractions Calculator tool to compute the GCF of 304/613, 160/138 i.e 16/84594 easily. The following is the detailed procedure to determine the greatest common factor of fractions 304/613, 160/138.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 304/613,160/138
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 304/613,160/138, numerators are 304,160
Denominators are 613,138
The GCF of 304,160 is 16 .
LCM of 613,138 is 84594.
The greatest common factor of 304/613,160/138 = [GCF of 304,160]/[LCM of 613,138]= 16/84594
Therefore, the GCF of 304/613,160/138 is 16/84594.
To find the highest common factor of 304,160, we have to find the factors of both numbers and list the highest common factor.
The factors of 304 are 1, 2, 4, 8, 16, 19, 38, 76, 152, 304
The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
The HCF of 304,160 is 16.
Lets's calculate GCF of 304,160
2 | 304, 160 |
2 | 152, 80 |
2 | 76, 40 |
2 | 38, 20 |
19, 10 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 = 16
Now, list down the factors of 304
:1,2,4,8,16,19,38,76,152,304
Now, list down the factors of 160
:1,2,4,5,8,10,16,20,32,40,80,160
Greatest Common Factor
We found the factors 304,160 . The biggest common factor number is the GCF number.
So the greatest common factor 304,160 is 16.
Lets's calculate LCM of 613,138
Given numbers has no common factors except 1. So, there LCM is their product i.e 84594
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 16/84594
Therefore, the GCF of Fractions 304/613,160/138 is 16/84594
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 613,138 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(613,138) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(613,138) x common factors =1 x 1 = 1
LCM(613,138) = ( 613 × 138 ) / 1
LCM(613,138) = 84594 / 1
LCM(613,138) = 84594
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 304,160?
The HCF of 304,160 is 16
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 304/613, 160/138?
Answer: GCF of Numerators as per given numbers 304/613, 160/138 is
GCF of Numerators i.e. for 304,160 is 16
LCM of denominators i.e. for 613,138 is 84594.
Thus, GCF of Fractions is 16/84594.Finally, GCF of Fractions for 304/613, 160/138 is 16/84594.