GCF of 513/77, 864/872
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 513/77, 864/872 i.e 27/67144 easily. The following is the detailed procedure to determine the greatest common factor of fractions 513/77, 864/872.
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 513/77,864/872?
Given fractions are 513/77,864/872
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 513/77,864/872, numerators are 513,864
Denominators are 77,872
The GCF of 513,864 is 27 .
LCM of 77,872 is 67144.
The greatest common factor of 513/77,864/872 = [GCF of 513,864]/[LCM of 77,872]= 27/67144
Therefore, the GCF of 513/77,864/872 is 27/67144.
To find the highest common factor of 513,864, we have to find the factors of both numbers and list the highest common factor.
The factors of 513 are 1, 3, 9, 19, 27, 57, 171, 513
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 HCF of 513,864 is 27.
Lets's calculate GCF of 513,864
| 3 | 513, 864 |
| 3 | 171, 288 |
| 3 | 57, 96 |
| 19, 32 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 513,864 By Matching Biggest Common Factor Method
Now, list down the factors of 513
:1,3,9,19,27,57,171,513
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
Greatest Common Factor
We found the factors 513,864 . The biggest common factor number is the GCF number.
So the greatest common factor 513,864 is 27.
Lets's calculate LCM of 77,872
Given numbers has no common factors except 1. So, there LCM is their product i.e 67144
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/67144
Therefore, the GCF of Fractions 513/77,864/872 is 27/67144
Least Common Multiple of 77,872 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 77,872 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(77,872) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(77,872) x common factors =1 x 1 = 1
LCM(77,872) = ( 77 × 872 ) / 1
LCM(77,872) = 67144 / 1
LCM(77,872) = 67144
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FAQs on GCF of Fractions of 513/77, 864/872
1. What is the HCF of 513,864?
The HCF of 513,864 is 27
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 513/77, 864/872?
Answer: GCF of Numerators as per given numbers 513/77, 864/872 is
GCF of Numerators i.e. for 513,864 is 27
LCM of denominators i.e. for 77,872 is 67144.
Thus, GCF of Fractions is 27/67144.Finally, GCF of Fractions for 513/77, 864/872 is 27/67144.