GCF of 5997/309, 5724/3177
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5997/309, 5724/3177 i.e 3/327231 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5997/309, 5724/3177.
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 5997/309,5724/3177?
Given fractions are 5997/309,5724/3177
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 5997/309,5724/3177, numerators are 5997,5724
Denominators are 309,3177
The GCF of 5997,5724 is 3 .
LCM of 309,3177 is 327231.
The greatest common factor of 5997/309,5724/3177 = [GCF of 5997,5724]/[LCM of 309,3177]= 3/327231
Therefore, the GCF of 5997/309,5724/3177 is 3/327231.
To find the highest common factor of 5997,5724, we have to find the factors of both numbers and list the highest common factor.
The factors of 5997 are 1, 3, 1999, 5997
The factors of 5724 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 53, 54, 106, 108, 159, 212, 318, 477, 636, 954, 1431, 1908, 2862, 5724
The HCF of 5997,5724 is 3.
Lets's calculate GCF of 5997,5724
| 3 | 5997, 5724 |
| 1999, 1908 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 5997,5724 By Matching Biggest Common Factor Method
Now, list down the factors of 5997
:1,3,1999,5997
Now, list down the factors of 5724
:1,2,3,4,6,9,12,18,27,36,53,54,106,108,159,212,318,477,636,954,1431,1908,2862,5724
Greatest Common Factor
We found the factors 5997,5724 . The biggest common factor number is the GCF number.
So the greatest common factor 5997,5724 is 3.
Lets's calculate LCM of 309,3177
| 3 | 309, 3177 |
| 103, 1059 |
∴ So the LCM of the given numbers is 3 x 103 x 1059 = 327231
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/327231
Therefore, the GCF of Fractions 5997/309,5724/3177 is 3/327231
Least Common Multiple of 309,3177 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 309,3177 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,3177) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,3177) x common factors =3 x 1 = 3
LCM(309,3177) = ( 309 × 3177 ) / 3
LCM(309,3177) = 981693 / 3
LCM(309,3177) = 327231
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FAQs on GCF of Fractions of 5997/309, 5724/3177
1. What is the HCF of 5997,5724?
The HCF of 5997,5724 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 5997/309, 5724/3177?
Answer: GCF of Numerators as per given numbers 5997/309, 5724/3177 is
GCF of Numerators i.e. for 5997,5724 is 3
LCM of denominators i.e. for 309,3177 is 327231.
Thus, GCF of Fractions is 3/327231.Finally, GCF of Fractions for 5997/309, 5724/3177 is 3/327231.