GCF of 225/512, 520/809
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 225/512, 520/809 i.e 5/414208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 225/512, 520/809.
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 225/512,520/809?
Given fractions are 225/512,520/809
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 225/512,520/809, numerators are 225,520
Denominators are 512,809
The GCF of 225,520 is 5 .
LCM of 512,809 is 414208.
The greatest common factor of 225/512,520/809 = [GCF of 225,520]/[LCM of 512,809]= 5/414208
Therefore, the GCF of 225/512,520/809 is 5/414208.
To find the highest common factor of 225,520, we have to find the factors of both numbers and list the highest common factor.
The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
The HCF of 225,520 is 5.
Lets's calculate GCF of 225,520
| 5 | 225, 520 |
| 45, 104 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 225,520 By Matching Biggest Common Factor Method
Now, list down the factors of 225
:1,3,5,9,15,25,45,75,225
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
Greatest Common Factor
We found the factors 225,520 . The biggest common factor number is the GCF number.
So the greatest common factor 225,520 is 5.
Lets's calculate LCM of 512,809
Given numbers has no common factors except 1. So, there LCM is their product i.e 414208
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/414208
Therefore, the GCF of Fractions 225/512,520/809 is 5/414208
Least Common Multiple of 512,809 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 512,809 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,809) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(512,809) x common factors =1 x 1 = 1
LCM(512,809) = ( 512 × 809 ) / 1
LCM(512,809) = 414208 / 1
LCM(512,809) = 414208
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FAQs on GCF of Fractions of 225/512, 520/809
1. What is the HCF of 225,520?
The HCF of 225,520 is 5
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 225/512, 520/809?
Answer: GCF of Numerators as per given numbers 225/512, 520/809 is
GCF of Numerators i.e. for 225,520 is 5
LCM of denominators i.e. for 512,809 is 414208.
Thus, GCF of Fractions is 5/414208.Finally, GCF of Fractions for 225/512, 520/809 is 5/414208.