Use our free GCF of Fractions Calculator tool to compute the GCF of 130/385, 342/574 i.e 2/31570 easily. The following is the detailed procedure to determine the greatest common factor of fractions 130/385, 342/574.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 130/385,342/574
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 130/385,342/574, numerators are 130,342
Denominators are 385,574
The GCF of 130,342 is 2 .
LCM of 385,574 is 31570.
The greatest common factor of 130/385,342/574 = [GCF of 130,342]/[LCM of 385,574]= 2/31570
Therefore, the GCF of 130/385,342/574 is 2/31570.
To find the highest common factor of 130,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 130,342 is 2.
Lets's calculate GCF of 130,342
2 | 130, 342 |
65, 171 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 130
:1,2,5,10,13,26,65,130
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 130,342 . The biggest common factor number is the GCF number.
So the greatest common factor 130,342 is 2.
Lets's calculate LCM of 385,574
7 | 385, 574 |
55, 82 |
∴ So the LCM of the given numbers is 7 x 55 x 82 = 31570
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/31570
Therefore, the GCF of Fractions 130/385,342/574 is 2/31570
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 385,574 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(385,574) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(385,574) x common factors =7 x 1 = 7
LCM(385,574) = ( 385 × 574 ) / 7
LCM(385,574) = 220990 / 7
LCM(385,574) = 31570
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 130,342?
The HCF of 130,342 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 130/385, 342/574?
Answer: GCF of Numerators as per given numbers 130/385, 342/574 is
GCF of Numerators i.e. for 130,342 is 2
LCM of denominators i.e. for 385,574 is 31570.
Thus, GCF of Fractions is 2/31570.Finally, GCF of Fractions for 130/385, 342/574 is 2/31570.