GCF of 285/327, 456/876
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 285/327, 456/876 i.e 57/95484 easily. The following is the detailed procedure to determine the greatest common factor of fractions 285/327, 456/876.
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 285/327,456/876?
Given fractions are 285/327,456/876
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 285/327,456/876, numerators are 285,456
Denominators are 327,876
The GCF of 285,456 is 57 .
LCM of 327,876 is 95484.
The greatest common factor of 285/327,456/876 = [GCF of 285,456]/[LCM of 327,876]= 57/95484
Therefore, the GCF of 285/327,456/876 is 57/95484.
To find the highest common factor of 285,456, we have to find the factors of both numbers and list the highest common factor.
The factors of 285 are 1, 3, 5, 15, 19, 57, 95, 285
The factors of 456 are 1, 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, 228, 456
The HCF of 285,456 is 57.
Lets's calculate GCF of 285,456
| 3 | 285, 456 |
| 19 | 95, 152 |
| 5, 8 |
∴ So the GCF of the given numbers is 3 x 19 = 57
Greatest Common Factor of 285,456 By Matching Biggest Common Factor Method
Now, list down the factors of 285
:1,3,5,15,19,57,95,285
Now, list down the factors of 456
:1,2,3,4,6,8,12,19,24,38,57,76,114,152,228,456
Greatest Common Factor
We found the factors 285,456 . The biggest common factor number is the GCF number.
So the greatest common factor 285,456 is 57.
Lets's calculate LCM of 327,876
| 3 | 327, 876 |
| 109, 292 |
∴ So the LCM of the given numbers is 3 x 109 x 292 = 95484
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 57/95484
Therefore, the GCF of Fractions 285/327,456/876 is 57/95484
Least Common Multiple of 327,876 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 327,876 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(327,876) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(327,876) x common factors =3 x 1 = 3
LCM(327,876) = ( 327 × 876 ) / 3
LCM(327,876) = 286452 / 3
LCM(327,876) = 95484
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FAQs on GCF of Fractions of 285/327, 456/876
1. What is the HCF of 285,456?
The HCF of 285,456 is 57
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 285/327, 456/876?
Answer: GCF of Numerators as per given numbers 285/327, 456/876 is
GCF of Numerators i.e. for 285,456 is 57
LCM of denominators i.e. for 327,876 is 95484.
Thus, GCF of Fractions is 57/95484.Finally, GCF of Fractions for 285/327, 456/876 is 57/95484.