Use our free GCF of Fractions Calculator tool to compute the GCF of 137/102, 582/328 i.e 1/16728 easily. The following is the detailed procedure to determine the greatest common factor of fractions 137/102, 582/328.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 137/102,582/328
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 137/102,582/328, numerators are 137,582
Denominators are 102,328
The GCF of 137,582 is 1 .
LCM of 102,328 is 16728.
The greatest common factor of 137/102,582/328 = [GCF of 137,582]/[LCM of 102,328]= 1/16728
Therefore, the GCF of 137/102,582/328 is 1/16728.
To find the highest common factor of 137,582, we have to find the factors of both numbers and list the highest common factor.
The factors of 137 are 1, 137
The factors of 582 are 1, 2, 3, 6, 97, 194, 291, 582
The HCF of 137,582 is 1.
Lets's calculate GCF of 137,582
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 137
:1,137
Now, list down the factors of 582
:1,2,3,6,97,194,291,582
Greatest Common Factor
We found the factors 137,582 . The biggest common factor number is the GCF number.
So the greatest common factor 137,582 is 1.
Lets's calculate LCM of 102,328
2 | 102, 328 |
51, 164 |
∴ So the LCM of the given numbers is 2 x 51 x 164 = 16728
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16728
Therefore, the GCF of Fractions 137/102,582/328 is 1/16728
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 102,328 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(102,328) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(102,328) x common factors =2 x 1 = 2
LCM(102,328) = ( 102 × 328 ) / 2
LCM(102,328) = 33456 / 2
LCM(102,328) = 16728
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 137,582?
The HCF of 137,582 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 137/102, 582/328?
Answer: GCF of Numerators as per given numbers 137/102, 582/328 is
GCF of Numerators i.e. for 137,582 is 1
LCM of denominators i.e. for 102,328 is 16728.
Thus, GCF of Fractions is 1/16728.Finally, GCF of Fractions for 137/102, 582/328 is 1/16728.