Use our free GCF of Fractions Calculator tool to compute the GCF of 265/209, 509/742 i.e 1/155078 easily. The following is the detailed procedure to determine the greatest common factor of fractions 265/209, 509/742.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 265/209,509/742
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 265/209,509/742, numerators are 265,509
Denominators are 209,742
The GCF of 265,509 is 1 .
LCM of 209,742 is 155078.
The greatest common factor of 265/209,509/742 = [GCF of 265,509]/[LCM of 209,742]= 1/155078
Therefore, the GCF of 265/209,509/742 is 1/155078.
To find the highest common factor of 265,509, we have to find the factors of both numbers and list the highest common factor.
The factors of 265 are 1, 5, 53, 265
The factors of 509 are 1, 509
The HCF of 265,509 is 1.
Lets's calculate GCF of 265,509
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 265
:1,5,53,265
Now, list down the factors of 509
:1,509
Greatest Common Factor
We found the factors 265,509 . The biggest common factor number is the GCF number.
So the greatest common factor 265,509 is 1.
Lets's calculate LCM of 209,742
Given numbers has no common factors except 1. So, there LCM is their product i.e 155078
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/155078
Therefore, the GCF of Fractions 265/209,509/742 is 1/155078
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 209,742 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(209,742) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(209,742) x common factors =1 x 1 = 1
LCM(209,742) = ( 209 × 742 ) / 1
LCM(209,742) = 155078 / 1
LCM(209,742) = 155078
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 265,509?
The HCF of 265,509 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 265/209, 509/742?
Answer: GCF of Numerators as per given numbers 265/209, 509/742 is
GCF of Numerators i.e. for 265,509 is 1
LCM of denominators i.e. for 209,742 is 155078.
Thus, GCF of Fractions is 1/155078.Finally, GCF of Fractions for 265/209, 509/742 is 1/155078.