GCF of 186/300, 7533/750
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 186/300, 7533/750 i.e 93/1500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 186/300, 7533/750.
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 186/300,7533/750?
Given fractions are 186/300,7533/750
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 186/300,7533/750, numerators are 186,7533
Denominators are 300,750
The GCF of 186,7533 is 93 .
LCM of 300,750 is 1500.
The greatest common factor of 186/300,7533/750 = [GCF of 186,7533]/[LCM of 300,750]= 93/1500
Therefore, the GCF of 186/300,7533/750 is 93/1500.
To find the highest common factor of 186,7533, we have to find the factors of both numbers and list the highest common factor.
The factors of 186 are 1, 2, 3, 6, 31, 62, 93, 186
The factors of 7533 are 1, 3, 9, 27, 31, 81, 93, 243, 279, 837, 2511, 7533
The HCF of 186,7533 is 93.
Lets's calculate GCF of 186,7533
| 3 | 186, 7533 |
| 31 | 62, 2511 |
| 2, 81 |
∴ So the GCF of the given numbers is 3 x 31 = 93
Greatest Common Factor of 186,7533 By Matching Biggest Common Factor Method
Now, list down the factors of 186
:1,2,3,6,31,62,93,186
Now, list down the factors of 7533
:1,3,9,27,31,81,93,243,279,837,2511,7533
Greatest Common Factor
We found the factors 186,7533 . The biggest common factor number is the GCF number.
So the greatest common factor 186,7533 is 93.
Lets's calculate LCM of 300,750
| 2 | 300, 750 |
| 3 | 150, 375 |
| 5 | 50, 125 |
| 5 | 10, 25 |
| 2, 5 |
∴ So the LCM of the given numbers is 2 x 3 x 5 x 5 x 2 x 5 = 1500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 93/1500
Therefore, the GCF of Fractions 186/300,7533/750 is 93/1500
Least Common Multiple of 300,750 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 300,750 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(300,750) = 150
common factors(in case of two or more numbers have common factors) = 1
GCF(300,750) x common factors =150 x 1 = 150
LCM(300,750) = ( 300 × 750 ) / 150
LCM(300,750) = 225000 / 150
LCM(300,750) = 1500
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 186/300, 7533/750
1. What is the HCF of 186,7533?
The HCF of 186,7533 is 93
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 186/300, 7533/750?
Answer: GCF of Numerators as per given numbers 186/300, 7533/750 is
GCF of Numerators i.e. for 186,7533 is 93
LCM of denominators i.e. for 300,750 is 1500.
Thus, GCF of Fractions is 93/1500.Finally, GCF of Fractions for 186/300, 7533/750 is 93/1500.