Use our free GCF of Fractions Calculator tool to compute the GCF of 469/260, 419/506 i.e 1/65780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 469/260, 419/506.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 469/260,419/506
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 469/260,419/506, numerators are 469,419
Denominators are 260,506
The GCF of 469,419 is 1 .
LCM of 260,506 is 65780.
The greatest common factor of 469/260,419/506 = [GCF of 469,419]/[LCM of 260,506]= 1/65780
Therefore, the GCF of 469/260,419/506 is 1/65780.
To find the highest common factor of 469,419, we have to find the factors of both numbers and list the highest common factor.
The factors of 469 are 1, 7, 67, 469
The factors of 419 are 1, 419
The HCF of 469,419 is 1.
Lets's calculate GCF of 469,419
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 469
:1,7,67,469
Now, list down the factors of 419
:1,419
Greatest Common Factor
We found the factors 469,419 . The biggest common factor number is the GCF number.
So the greatest common factor 469,419 is 1.
Lets's calculate LCM of 260,506
2 | 260, 506 |
130, 253 |
∴ So the LCM of the given numbers is 2 x 130 x 253 = 65780
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/65780
Therefore, the GCF of Fractions 469/260,419/506 is 1/65780
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 260,506 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(260,506) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(260,506) x common factors =2 x 1 = 2
LCM(260,506) = ( 260 × 506 ) / 2
LCM(260,506) = 131560 / 2
LCM(260,506) = 65780
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 469,419?
The HCF of 469,419 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 469/260, 419/506?
Answer: GCF of Numerators as per given numbers 469/260, 419/506 is
GCF of Numerators i.e. for 469,419 is 1
LCM of denominators i.e. for 260,506 is 65780.
Thus, GCF of Fractions is 1/65780.Finally, GCF of Fractions for 469/260, 419/506 is 1/65780.