GCF of 7125/405, 3600/9681
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7125/405, 3600/9681 i.e 75/1306935 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7125/405, 3600/9681.
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 7125/405,3600/9681?
Given fractions are 7125/405,3600/9681
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 7125/405,3600/9681, numerators are 7125,3600
Denominators are 405,9681
The GCF of 7125,3600 is 75 .
LCM of 405,9681 is 1306935.
The greatest common factor of 7125/405,3600/9681 = [GCF of 7125,3600]/[LCM of 405,9681]= 75/1306935
Therefore, the GCF of 7125/405,3600/9681 is 75/1306935.
To find the highest common factor of 7125,3600, we have to find the factors of both numbers and list the highest common factor.
The factors of 7125 are 1, 3, 5, 15, 19, 25, 57, 75, 95, 125, 285, 375, 475, 1425, 2375, 7125
The factors of 3600 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 36, 40, 45, 48, 50, 60, 72, 75, 80, 90, 100, 120, 144, 150, 180, 200, 225, 240, 300, 360, 400, 450, 600, 720, 900, 1200, 1800, 3600
The HCF of 7125,3600 is 75.
Lets's calculate GCF of 7125,3600
| 3 | 7125, 3600 |
| 5 | 2375, 1200 |
| 5 | 475, 240 |
| 95, 48 |
∴ So the GCF of the given numbers is 3 x 5 x 5 = 75
Greatest Common Factor of 7125,3600 By Matching Biggest Common Factor Method
Now, list down the factors of 7125
:1,3,5,15,19,25,57,75,95,125,285,375,475,1425,2375,7125
Now, list down the factors of 3600
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,25,30,36,40,45,48,50,60,72,75,80,90,100,120,144,150,180,200,225,240,300,360,400,450,600,720,900,1200,1800,3600
Greatest Common Factor
We found the factors 7125,3600 . The biggest common factor number is the GCF number.
So the greatest common factor 7125,3600 is 75.
Lets's calculate LCM of 405,9681
| 3 | 405, 9681 |
| 135, 3227 |
∴ So the LCM of the given numbers is 3 x 135 x 3227 = 1306935
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 75/1306935
Therefore, the GCF of Fractions 7125/405,3600/9681 is 75/1306935
Least Common Multiple of 405,9681 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 405,9681 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(405,9681) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(405,9681) x common factors =3 x 1 = 3
LCM(405,9681) = ( 405 × 9681 ) / 3
LCM(405,9681) = 3920805 / 3
LCM(405,9681) = 1306935
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FAQs on GCF of Fractions of 7125/405, 3600/9681
1. What is the HCF of 7125,3600?
The HCF of 7125,3600 is 75
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 7125/405, 3600/9681?
Answer: GCF of Numerators as per given numbers 7125/405, 3600/9681 is
GCF of Numerators i.e. for 7125,3600 is 75
LCM of denominators i.e. for 405,9681 is 1306935.
Thus, GCF of Fractions is 75/1306935.Finally, GCF of Fractions for 7125/405, 3600/9681 is 75/1306935.