GCF of 365/521, 409/282
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 365/521, 409/282 i.e 1/146922 easily. The following is the detailed procedure to determine the greatest common factor of fractions 365/521, 409/282.
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 365/521,409/282?
Given fractions are 365/521,409/282
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 365/521,409/282, numerators are 365,409
Denominators are 521,282
The GCF of 365,409 is 1 .
LCM of 521,282 is 146922.
The greatest common factor of 365/521,409/282 = [GCF of 365,409]/[LCM of 521,282]= 1/146922
Therefore, the GCF of 365/521,409/282 is 1/146922.
To find the highest common factor of 365,409, we have to find the factors of both numbers and list the highest common factor.
The factors of 365 are 1, 5, 73, 365
The factors of 409 are 1, 409
The HCF of 365,409 is 1.
Lets's calculate GCF of 365,409
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 365,409 By Matching Biggest Common Factor Method
Now, list down the factors of 365
:1,5,73,365
Now, list down the factors of 409
:1,409
Greatest Common Factor
We found the factors 365,409 . The biggest common factor number is the GCF number.
So the greatest common factor 365,409 is 1.
Lets's calculate LCM of 521,282
Given numbers has no common factors except 1. So, there LCM is their product i.e 146922
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/146922
Therefore, the GCF of Fractions 365/521,409/282 is 1/146922
Least Common Multiple of 521,282 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 521,282 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(521,282) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(521,282) x common factors =1 x 1 = 1
LCM(521,282) = ( 521 × 282 ) / 1
LCM(521,282) = 146922 / 1
LCM(521,282) = 146922
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 365/521, 409/282
1. What is the HCF of 365,409?
The HCF of 365,409 is 1
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 365/521, 409/282?
Answer: GCF of Numerators as per given numbers 365/521, 409/282 is
GCF of Numerators i.e. for 365,409 is 1
LCM of denominators i.e. for 521,282 is 146922.
Thus, GCF of Fractions is 1/146922.Finally, GCF of Fractions for 365/521, 409/282 is 1/146922.