GCF of 5280/591, 6900/819
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5280/591, 6900/819 i.e 60/161343 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5280/591, 6900/819.
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 5280/591,6900/819?
Given fractions are 5280/591,6900/819
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 5280/591,6900/819, numerators are 5280,6900
Denominators are 591,819
The GCF of 5280,6900 is 60 .
LCM of 591,819 is 161343.
The greatest common factor of 5280/591,6900/819 = [GCF of 5280,6900]/[LCM of 591,819]= 60/161343
Therefore, the GCF of 5280/591,6900/819 is 60/161343.
To find the highest common factor of 5280,6900, we have to find the factors of both numbers and list the highest common factor.
The factors of 5280 are 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 15, 16, 20, 22, 24, 30, 32, 33, 40, 44, 48, 55, 60, 66, 80, 88, 96, 110, 120, 132, 160, 165, 176, 220, 240, 264, 330, 352, 440, 480, 528, 660, 880, 1056, 1320, 1760, 2640, 5280
The factors of 6900 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 23, 25, 30, 46, 50, 60, 69, 75, 92, 100, 115, 138, 150, 230, 276, 300, 345, 460, 575, 690, 1150, 1380, 1725, 2300, 3450, 6900
The HCF of 5280,6900 is 60.
Lets's calculate GCF of 5280,6900
| 2 | 5280, 6900 |
| 2 | 2640, 3450 |
| 3 | 1320, 1725 |
| 5 | 440, 575 |
| 88, 115 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Greatest Common Factor of 5280,6900 By Matching Biggest Common Factor Method
Now, list down the factors of 5280
:1,2,3,4,5,6,8,10,11,12,15,16,20,22,24,30,32,33,40,44,48,55,60,66,80,88,96,110,120,132,160,165,176,220,240,264,330,352,440,480,528,660,880,1056,1320,1760,2640,5280
Now, list down the factors of 6900
:1,2,3,4,5,6,10,12,15,20,23,25,30,46,50,60,69,75,92,100,115,138,150,230,276,300,345,460,575,690,1150,1380,1725,2300,3450,6900
Greatest Common Factor
We found the factors 5280,6900 . The biggest common factor number is the GCF number.
So the greatest common factor 5280,6900 is 60.
Lets's calculate LCM of 591,819
| 3 | 591, 819 |
| 197, 273 |
∴ So the LCM of the given numbers is 3 x 197 x 273 = 161343
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/161343
Therefore, the GCF of Fractions 5280/591,6900/819 is 60/161343
Least Common Multiple of 591,819 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 591,819 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(591,819) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(591,819) x common factors =3 x 1 = 3
LCM(591,819) = ( 591 × 819 ) / 3
LCM(591,819) = 484029 / 3
LCM(591,819) = 161343
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FAQs on GCF of Fractions of 5280/591, 6900/819
1. What is the HCF of 5280,6900?
The HCF of 5280,6900 is 60
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 5280/591, 6900/819?
Answer: GCF of Numerators as per given numbers 5280/591, 6900/819 is
GCF of Numerators i.e. for 5280,6900 is 60
LCM of denominators i.e. for 591,819 is 161343.
Thus, GCF of Fractions is 60/161343.Finally, GCF of Fractions for 5280/591, 6900/819 is 60/161343.