Use our free GCF of Fractions Calculator tool to compute the GCF of 649/507, 590/143 i.e 59/5577 easily. The following is the detailed procedure to determine the greatest common factor of fractions 649/507, 590/143.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 649/507,590/143
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 649/507,590/143, numerators are 649,590
Denominators are 507,143
The GCF of 649,590 is 59 .
LCM of 507,143 is 5577.
The greatest common factor of 649/507,590/143 = [GCF of 649,590]/[LCM of 507,143]= 59/5577
Therefore, the GCF of 649/507,590/143 is 59/5577.
To find the highest common factor of 649,590, we have to find the factors of both numbers and list the highest common factor.
The factors of 649 are 1, 11, 59, 649
The factors of 590 are 1, 2, 5, 10, 59, 118, 295, 590
The HCF of 649,590 is 59.
Lets's calculate GCF of 649,590
59 | 649, 590 |
11, 10 |
∴ So the GCF of the given numbers is 59 = 59
Now, list down the factors of 649
:1,11,59,649
Now, list down the factors of 590
:1,2,5,10,59,118,295,590
Greatest Common Factor
We found the factors 649,590 . The biggest common factor number is the GCF number.
So the greatest common factor 649,590 is 59.
Lets's calculate LCM of 507,143
13 | 507, 143 |
39, 11 |
∴ So the LCM of the given numbers is 13 x 39 x 11 = 5577
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 59/5577
Therefore, the GCF of Fractions 649/507,590/143 is 59/5577
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 507,143 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(507,143) = 13
common factors(in case of two or more numbers have common factors) = 1
GCF(507,143) x common factors =13 x 1 = 13
LCM(507,143) = ( 507 × 143 ) / 13
LCM(507,143) = 72501 / 13
LCM(507,143) = 5577
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 649,590?
The HCF of 649,590 is 59
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 649/507, 590/143?
Answer: GCF of Numerators as per given numbers 649/507, 590/143 is
GCF of Numerators i.e. for 649,590 is 59
LCM of denominators i.e. for 507,143 is 5577.
Thus, GCF of Fractions is 59/5577.Finally, GCF of Fractions for 649/507, 590/143 is 59/5577.