Use our free GCF of Fractions Calculator tool to compute the GCF of 319/130, 130/234 i.e 1/1170 easily. The following is the detailed procedure to determine the greatest common factor of fractions 319/130, 130/234.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 319/130,130/234
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 319/130,130/234, numerators are 319,130
Denominators are 130,234
The GCF of 319,130 is 1 .
LCM of 130,234 is 1170.
The greatest common factor of 319/130,130/234 = [GCF of 319,130]/[LCM of 130,234]= 1/1170
Therefore, the GCF of 319/130,130/234 is 1/1170.
To find the highest common factor of 319,130, we have to find the factors of both numbers and list the highest common factor.
The factors of 319 are 1, 11, 29, 319
The factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130
The HCF of 319,130 is 1.
Lets's calculate GCF of 319,130
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 319
:1,11,29,319
Now, list down the factors of 130
:1,2,5,10,13,26,65,130
Greatest Common Factor
We found the factors 319,130 . The biggest common factor number is the GCF number.
So the greatest common factor 319,130 is 1.
Lets's calculate LCM of 130,234
2 | 130, 234 |
13 | 65, 117 |
5, 9 |
∴ So the LCM of the given numbers is 2 x 13 x 5 x 9 = 1170
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1170
Therefore, the GCF of Fractions 319/130,130/234 is 1/1170
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 130,234 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(130,234) = 26
common factors(in case of two or more numbers have common factors) = 1
GCF(130,234) x common factors =26 x 1 = 26
LCM(130,234) = ( 130 × 234 ) / 26
LCM(130,234) = 30420 / 26
LCM(130,234) = 1170
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 319,130?
The HCF of 319,130 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 319/130, 130/234?
Answer: GCF of Numerators as per given numbers 319/130, 130/234 is
GCF of Numerators i.e. for 319,130 is 1
LCM of denominators i.e. for 130,234 is 1170.
Thus, GCF of Fractions is 1/1170.Finally, GCF of Fractions for 319/130, 130/234 is 1/1170.