Use our free GCF of Fractions Calculator tool to compute the GCF of 490/602, 509/428 i.e 1/128828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 490/602, 509/428.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 490/602,509/428
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 490/602,509/428, numerators are 490,509
Denominators are 602,428
The GCF of 490,509 is 1 .
LCM of 602,428 is 128828.
The greatest common factor of 490/602,509/428 = [GCF of 490,509]/[LCM of 602,428]= 1/128828
Therefore, the GCF of 490/602,509/428 is 1/128828.
To find the highest common factor of 490,509, we have to find the factors of both numbers and list the highest common factor.
The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490
The factors of 509 are 1, 509
The HCF of 490,509 is 1.
Lets's calculate GCF of 490,509
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 490
:1,2,5,7,10,14,35,49,70,98,245,490
Now, list down the factors of 509
:1,509
Greatest Common Factor
We found the factors 490,509 . The biggest common factor number is the GCF number.
So the greatest common factor 490,509 is 1.
Lets's calculate LCM of 602,428
2 | 602, 428 |
301, 214 |
∴ So the LCM of the given numbers is 2 x 301 x 214 = 128828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/128828
Therefore, the GCF of Fractions 490/602,509/428 is 1/128828
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 602,428 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(602,428) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(602,428) x common factors =2 x 1 = 2
LCM(602,428) = ( 602 × 428 ) / 2
LCM(602,428) = 257656 / 2
LCM(602,428) = 128828
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 490,509?
The HCF of 490,509 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 490/602, 509/428?
Answer: GCF of Numerators as per given numbers 490/602, 509/428 is
GCF of Numerators i.e. for 490,509 is 1
LCM of denominators i.e. for 602,428 is 128828.
Thus, GCF of Fractions is 1/128828.Finally, GCF of Fractions for 490/602, 509/428 is 1/128828.