Use our free GCF of Fractions Calculator tool to compute the GCF of 609/652, 105/164 i.e 21/26732 easily. The following is the detailed procedure to determine the greatest common factor of fractions 609/652, 105/164.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 609/652,105/164
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 609/652,105/164, numerators are 609,105
Denominators are 652,164
The GCF of 609,105 is 21 .
LCM of 652,164 is 26732.
The greatest common factor of 609/652,105/164 = [GCF of 609,105]/[LCM of 652,164]= 21/26732
Therefore, the GCF of 609/652,105/164 is 21/26732.
To find the highest common factor of 609,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 609,105 is 21.
Lets's calculate GCF of 609,105
3 | 609, 105 |
7 | 203, 35 |
29, 5 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 609,105 . The biggest common factor number is the GCF number.
So the greatest common factor 609,105 is 21.
Lets's calculate LCM of 652,164
2 | 652, 164 |
2 | 326, 82 |
163, 41 |
∴ So the LCM of the given numbers is 2 x 2 x 163 x 41 = 26732
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/26732
Therefore, the GCF of Fractions 609/652,105/164 is 21/26732
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 652,164 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(652,164) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(652,164) x common factors =4 x 1 = 4
LCM(652,164) = ( 652 × 164 ) / 4
LCM(652,164) = 106928 / 4
LCM(652,164) = 26732
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 609,105?
The HCF of 609,105 is 21
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 609/652, 105/164?
Answer: GCF of Numerators as per given numbers 609/652, 105/164 is
GCF of Numerators i.e. for 609,105 is 21
LCM of denominators i.e. for 652,164 is 26732.
Thus, GCF of Fractions is 21/26732.Finally, GCF of Fractions for 609/652, 105/164 is 21/26732.