Use our free GCF of Fractions Calculator tool to compute the GCF of 522/165, 1015/2271 i.e 29/124905 easily. The following is the detailed procedure to determine the greatest common factor of fractions 522/165, 1015/2271.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 522/165,1015/2271
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 522/165,1015/2271, numerators are 522,1015
Denominators are 165,2271
The GCF of 522,1015 is 29 .
LCM of 165,2271 is 124905.
The greatest common factor of 522/165,1015/2271 = [GCF of 522,1015]/[LCM of 165,2271]= 29/124905
Therefore, the GCF of 522/165,1015/2271 is 29/124905.
To find the highest common factor of 522,1015, 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 1015 are 1, 5, 7, 29, 35, 145, 203, 1015
The HCF of 522,1015 is 29.
Lets's calculate GCF of 522,1015
29 | 522, 1015 |
18, 35 |
∴ So the GCF of the given numbers is 29 = 29
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 1015
:1,5,7,29,35,145,203,1015
Greatest Common Factor
We found the factors 522,1015 . The biggest common factor number is the GCF number.
So the greatest common factor 522,1015 is 29.
Lets's calculate LCM of 165,2271
3 | 165, 2271 |
55, 757 |
∴ So the LCM of the given numbers is 3 x 55 x 757 = 124905
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 29/124905
Therefore, the GCF of Fractions 522/165,1015/2271 is 29/124905
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 165,2271 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(165,2271) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(165,2271) x common factors =3 x 1 = 3
LCM(165,2271) = ( 165 × 2271 ) / 3
LCM(165,2271) = 374715 / 3
LCM(165,2271) = 124905
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 522,1015?
The HCF of 522,1015 is 29
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 522/165, 1015/2271?
Answer: GCF of Numerators as per given numbers 522/165, 1015/2271 is
GCF of Numerators i.e. for 522,1015 is 29
LCM of denominators i.e. for 165,2271 is 124905.
Thus, GCF of Fractions is 29/124905.Finally, GCF of Fractions for 522/165, 1015/2271 is 29/124905.