Use our free GCF of Fractions Calculator tool to compute the GCF of 11/78, 65/114, 468/320 i.e 1/237120 easily. The following is the detailed procedure to determine the greatest common factor of fractions 11/78, 65/114, 468/320.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 11/78,65/114,468/320
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 11/78,65/114,468/320, numerators are 11,65,468
Denominators are 78,114,320
The GCF of 11,65,468 is 1 .
LCM of 78,114,320 is 237120.
The greatest common factor of 11/78,65/114,468/320 = [GCF of 11,65,468]/[LCM of 78,114,320]= 1/237120
Therefore, the GCF of 11/78,65/114,468/320 is 1/237120.
To find the highest common factor of 11,65,468, we have to find the factors of both numbers and list the highest common factor.
The factors of 11 are 1, 11
The factors of 65 are 1, 5, 13, 65
The factors of 468 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, 234, 468
The HCF of 11,65,468 is 1.
Lets's calculate GCF of 11,65,468
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 11
:1,11
Now, list down the factors of 65
:1,5,13,65
Now, list down the factors of 468
:1,2,3,4,6,9,12,13,18,26,36,39,52,78,117,156,234,468
Greatest Common Factor
We found the factors 11,65,468 . The biggest common factor number is the GCF number.
So the greatest common factor 11,65,468 is 1.
Lets's calculate LCM of 78,114,320
2 | 78, 114, 320 |
3 | 39, 57, 160 |
13, 19, 160 |
∴ So the LCM of the given numbers is 2 x 3 x 13 x 19 x 160 = 237120
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/237120
Therefore, the GCF of Fractions 11/78,65/114,468/320 is 1/237120
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 78,114,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(78,114,320) = 2
common factors(in case of two or more numbers have common factors) = 6
GCF(78,114,320) x common factors =2 x 6 = 12
LCM(78,114,320) = ( 78 × 114 × 320 ) / 12
LCM(78,114,320) = 2845440 / 12
LCM(78,114,320) = 237120
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 11,65,468?
The HCF of 11,65,468 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 11/78, 65/114, 468/320?
Answer: GCF of Numerators as per given numbers 11/78, 65/114, 468/320 is
GCF of Numerators i.e. for 11,65,468 is 1
LCM of denominators i.e. for 78,114,320 is 237120.
Thus, GCF of Fractions is 1/237120.Finally, GCF of Fractions for 11/78, 65/114, 468/320 is 1/237120.