GCF of 324/69, 120/5823
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 324/69, 120/5823 i.e 12/133929 easily. The following is the detailed procedure to determine the greatest common factor of fractions 324/69, 120/5823.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 324/69,120/5823?
Given fractions are 324/69,120/5823
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 324/69,120/5823, numerators are 324,120
Denominators are 69,5823
The GCF of 324,120 is 12 .
LCM of 69,5823 is 133929.
The greatest common factor of 324/69,120/5823 = [GCF of 324,120]/[LCM of 69,5823]= 12/133929
Therefore, the GCF of 324/69,120/5823 is 12/133929.
To find the highest common factor of 324,120, we have to find the factors of both numbers and list the highest common factor.
The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
The HCF of 324,120 is 12.
Lets's calculate GCF of 324,120
| 2 | 324, 120 |
| 2 | 162, 60 |
| 3 | 81, 30 |
| 27, 10 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 324,120 By Matching Biggest Common Factor Method
Now, list down the factors of 324
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,324
Now, list down the factors of 120
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120
Greatest Common Factor
We found the factors 324,120 . The biggest common factor number is the GCF number.
So the greatest common factor 324,120 is 12.
Lets's calculate LCM of 69,5823
| 3 | 69, 5823 |
| 23, 1941 |
∴ So the LCM of the given numbers is 3 x 23 x 1941 = 133929
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/133929
Therefore, the GCF of Fractions 324/69,120/5823 is 12/133929
Least Common Multiple of 69,5823 with GCF Formula
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 69,5823 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,5823) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(69,5823) x common factors =3 x 1 = 3
LCM(69,5823) = ( 69 × 5823 ) / 3
LCM(69,5823) = 401787 / 3
LCM(69,5823) = 133929
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 324/69, 120/5823
1. What is the HCF of 324,120?
The HCF of 324,120 is 12
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 324/69, 120/5823?
Answer: GCF of Numerators as per given numbers 324/69, 120/5823 is
GCF of Numerators i.e. for 324,120 is 12
LCM of denominators i.e. for 69,5823 is 133929.
Thus, GCF of Fractions is 12/133929.Finally, GCF of Fractions for 324/69, 120/5823 is 12/133929.