GCF of 5757/600, 6816/7544
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5757/600, 6816/7544 i.e 3/565800 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5757/600, 6816/7544.
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 5757/600,6816/7544?
Given fractions are 5757/600,6816/7544
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 5757/600,6816/7544, numerators are 5757,6816
Denominators are 600,7544
The GCF of 5757,6816 is 3 .
LCM of 600,7544 is 565800.
The greatest common factor of 5757/600,6816/7544 = [GCF of 5757,6816]/[LCM of 600,7544]= 3/565800
Therefore, the GCF of 5757/600,6816/7544 is 3/565800.
To find the highest common factor of 5757,6816, we have to find the factors of both numbers and list the highest common factor.
The factors of 5757 are 1, 3, 19, 57, 101, 303, 1919, 5757
The factors of 6816 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 71, 96, 142, 213, 284, 426, 568, 852, 1136, 1704, 2272, 3408, 6816
The HCF of 5757,6816 is 3.
Lets's calculate GCF of 5757,6816
| 3 | 5757, 6816 |
| 1919, 2272 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 5757,6816 By Matching Biggest Common Factor Method
Now, list down the factors of 5757
:1,3,19,57,101,303,1919,5757
Now, list down the factors of 6816
:1,2,3,4,6,8,12,16,24,32,48,71,96,142,213,284,426,568,852,1136,1704,2272,3408,6816
Greatest Common Factor
We found the factors 5757,6816 . The biggest common factor number is the GCF number.
So the greatest common factor 5757,6816 is 3.
Lets's calculate LCM of 600,7544
| 2 | 600, 7544 |
| 2 | 300, 3772 |
| 2 | 150, 1886 |
| 75, 943 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 75 x 943 = 565800
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/565800
Therefore, the GCF of Fractions 5757/600,6816/7544 is 3/565800
Least Common Multiple of 600,7544 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 600,7544 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(600,7544) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(600,7544) x common factors =8 x 1 = 8
LCM(600,7544) = ( 600 × 7544 ) / 8
LCM(600,7544) = 4526400 / 8
LCM(600,7544) = 565800
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FAQs on GCF of Fractions of 5757/600, 6816/7544
1. What is the HCF of 5757,6816?
The HCF of 5757,6816 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 5757/600, 6816/7544?
Answer: GCF of Numerators as per given numbers 5757/600, 6816/7544 is
GCF of Numerators i.e. for 5757,6816 is 3
LCM of denominators i.e. for 600,7544 is 565800.
Thus, GCF of Fractions is 3/565800.Finally, GCF of Fractions for 5757/600, 6816/7544 is 3/565800.