GCF of 575/360, 600/400
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 575/360, 600/400 i.e 25/3600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 575/360, 600/400.
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 575/360,600/400?
Given fractions are 575/360,600/400
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 575/360,600/400, numerators are 575,600
Denominators are 360,400
The GCF of 575,600 is 25 .
LCM of 360,400 is 3600.
The greatest common factor of 575/360,600/400 = [GCF of 575,600]/[LCM of 360,400]= 25/3600
Therefore, the GCF of 575/360,600/400 is 25/3600.
To find the highest common factor of 575,600, we have to find the factors of both numbers and list the highest common factor.
The factors of 575 are 1, 5, 23, 25, 115, 575
The factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
The HCF of 575,600 is 25.
Lets's calculate GCF of 575,600
| 5 | 575, 600 |
| 5 | 115, 120 |
| 23, 24 |
∴ So the GCF of the given numbers is 5 x 5 = 25
Greatest Common Factor of 575,600 By Matching Biggest Common Factor Method
Now, list down the factors of 575
:1,5,23,25,115,575
Now, list down the factors of 600
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600
Greatest Common Factor
We found the factors 575,600 . The biggest common factor number is the GCF number.
So the greatest common factor 575,600 is 25.
Lets's calculate LCM of 360,400
| 2 | 360, 400 |
| 2 | 180, 200 |
| 2 | 90, 100 |
| 5 | 45, 50 |
| 9, 10 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 9 x 10 = 3600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/3600
Therefore, the GCF of Fractions 575/360,600/400 is 25/3600
Least Common Multiple of 360,400 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 360,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(360,400) = 40
common factors(in case of two or more numbers have common factors) = 1
GCF(360,400) x common factors =40 x 1 = 40
LCM(360,400) = ( 360 × 400 ) / 40
LCM(360,400) = 144000 / 40
LCM(360,400) = 3600
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FAQs on GCF of Fractions of 575/360, 600/400
1. What is the HCF of 575,600?
The HCF of 575,600 is 25
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 575/360, 600/400?
Answer: GCF of Numerators as per given numbers 575/360, 600/400 is
GCF of Numerators i.e. for 575,600 is 25
LCM of denominators i.e. for 360,400 is 3600.
Thus, GCF of Fractions is 25/3600.Finally, GCF of Fractions for 575/360, 600/400 is 25/3600.