Use our free GCF of Fractions Calculator tool to compute the GCF of 522/609, 735/254 i.e 3/154686 easily. The following is the detailed procedure to determine the greatest common factor of fractions 522/609, 735/254.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 522/609,735/254
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 522/609,735/254, numerators are 522,735
Denominators are 609,254
The GCF of 522,735 is 3 .
LCM of 609,254 is 154686.
The greatest common factor of 522/609,735/254 = [GCF of 522,735]/[LCM of 609,254]= 3/154686
Therefore, the GCF of 522/609,735/254 is 3/154686.
To find the highest common factor of 522,735, we have to find the factors of both numbers and list the highest common factor.
The factors of 522 are 1, 2, 3, 6, 9, 18, 29, 58, 87, 174, 261, 522
The factors of 735 are 1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 735
The HCF of 522,735 is 3.
Lets's calculate GCF of 522,735
3 | 522, 735 |
174, 245 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 522
:1,2,3,6,9,18,29,58,87,174,261,522
Now, list down the factors of 735
:1,3,5,7,15,21,35,49,105,147,245,735
Greatest Common Factor
We found the factors 522,735 . The biggest common factor number is the GCF number.
So the greatest common factor 522,735 is 3.
Lets's calculate LCM of 609,254
Given numbers has no common factors except 1. So, there LCM is their product i.e 154686
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/154686
Therefore, the GCF of Fractions 522/609,735/254 is 3/154686
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 609,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(609,254) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(609,254) x common factors =1 x 1 = 1
LCM(609,254) = ( 609 × 254 ) / 1
LCM(609,254) = 154686 / 1
LCM(609,254) = 154686
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 522,735?
The HCF of 522,735 is 3
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 522/609, 735/254?
Answer: GCF of Numerators as per given numbers 522/609, 735/254 is
GCF of Numerators i.e. for 522,735 is 3
LCM of denominators i.e. for 609,254 is 154686.
Thus, GCF of Fractions is 3/154686.Finally, GCF of Fractions for 522/609, 735/254 is 3/154686.