Use our free GCF of Fractions Calculator tool to compute the GCF of 411/127, 465/115 i.e 3/14605 easily. The following is the detailed procedure to determine the greatest common factor of fractions 411/127, 465/115.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 411/127,465/115
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 411/127,465/115, numerators are 411,465
Denominators are 127,115
The GCF of 411,465 is 3 .
LCM of 127,115 is 14605.
The greatest common factor of 411/127,465/115 = [GCF of 411,465]/[LCM of 127,115]= 3/14605
Therefore, the GCF of 411/127,465/115 is 3/14605.
To find the highest common factor of 411,465, we have to find the factors of both numbers and list the highest common factor.
The factors of 411 are 1, 3, 137, 411
The factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465
The HCF of 411,465 is 3.
Lets's calculate GCF of 411,465
3 | 411, 465 |
137, 155 |
∴ So the GCF of the given numbers is 3 = 3
Now, list down the factors of 411
:1,3,137,411
Now, list down the factors of 465
:1,3,5,15,31,93,155,465
Greatest Common Factor
We found the factors 411,465 . The biggest common factor number is the GCF number.
So the greatest common factor 411,465 is 3.
Lets's calculate LCM of 127,115
Given numbers has no common factors except 1. So, there LCM is their product i.e 14605
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/14605
Therefore, the GCF of Fractions 411/127,465/115 is 3/14605
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 127,115 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(127,115) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(127,115) x common factors =1 x 1 = 1
LCM(127,115) = ( 127 × 115 ) / 1
LCM(127,115) = 14605 / 1
LCM(127,115) = 14605
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 411,465?
The HCF of 411,465 is 3
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 411/127, 465/115?
Answer: GCF of Numerators as per given numbers 411/127, 465/115 is
GCF of Numerators i.e. for 411,465 is 3
LCM of denominators i.e. for 127,115 is 14605.
Thus, GCF of Fractions is 3/14605.Finally, GCF of Fractions for 411/127, 465/115 is 3/14605.