GCF of 864/975, 231/189
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 864/975, 231/189 i.e 3/61425 easily. The following is the detailed procedure to determine the greatest common factor of fractions 864/975, 231/189.
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 864/975,231/189?
Given fractions are 864/975,231/189
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 864/975,231/189, numerators are 864,231
Denominators are 975,189
The GCF of 864,231 is 3 .
LCM of 975,189 is 61425.
The greatest common factor of 864/975,231/189 = [GCF of 864,231]/[LCM of 975,189]= 3/61425
Therefore, the GCF of 864/975,231/189 is 3/61425.
To find the highest common factor of 864,231, we have to find the factors of both numbers and list the highest common factor.
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The HCF of 864,231 is 3.
Lets's calculate GCF of 864,231
| 3 | 864, 231 |
| 288, 77 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 864,231 By Matching Biggest Common Factor Method
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Greatest Common Factor
We found the factors 864,231 . The biggest common factor number is the GCF number.
So the greatest common factor 864,231 is 3.
Lets's calculate LCM of 975,189
| 3 | 975, 189 |
| 325, 63 |
∴ So the LCM of the given numbers is 3 x 325 x 63 = 61425
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/61425
Therefore, the GCF of Fractions 864/975,231/189 is 3/61425
Least Common Multiple of 975,189 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 975,189 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(975,189) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(975,189) x common factors =3 x 1 = 3
LCM(975,189) = ( 975 × 189 ) / 3
LCM(975,189) = 184275 / 3
LCM(975,189) = 61425
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FAQs on GCF of Fractions of 864/975, 231/189
1. What is the HCF of 864,231?
The HCF of 864,231 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 864/975, 231/189?
Answer: GCF of Numerators as per given numbers 864/975, 231/189 is
GCF of Numerators i.e. for 864,231 is 3
LCM of denominators i.e. for 975,189 is 61425.
Thus, GCF of Fractions is 3/61425.Finally, GCF of Fractions for 864/975, 231/189 is 3/61425.