GCF of 273/405, 506/369
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 273/405, 506/369 i.e 1/16605 easily. The following is the detailed procedure to determine the greatest common factor of fractions 273/405, 506/369.
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 273/405,506/369?
Given fractions are 273/405,506/369
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 273/405,506/369, numerators are 273,506
Denominators are 405,369
The GCF of 273,506 is 1 .
LCM of 405,369 is 16605.
The greatest common factor of 273/405,506/369 = [GCF of 273,506]/[LCM of 405,369]= 1/16605
Therefore, the GCF of 273/405,506/369 is 1/16605.
To find the highest common factor of 273,506, we have to find the factors of both numbers and list the highest common factor.
The factors of 273 are 1, 3, 7, 13, 21, 39, 91, 273
The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506
The HCF of 273,506 is 1.
Lets's calculate GCF of 273,506
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 273,506 By Matching Biggest Common Factor Method
Now, list down the factors of 273
:1,3,7,13,21,39,91,273
Now, list down the factors of 506
:1,2,11,22,23,46,253,506
Greatest Common Factor
We found the factors 273,506 . The biggest common factor number is the GCF number.
So the greatest common factor 273,506 is 1.
Lets's calculate LCM of 405,369
| 3 | 405, 369 |
| 3 | 135, 123 |
| 45, 41 |
∴ So the LCM of the given numbers is 3 x 3 x 45 x 41 = 16605
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16605
Therefore, the GCF of Fractions 273/405,506/369 is 1/16605
Least Common Multiple of 405,369 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 405,369 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(405,369) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(405,369) x common factors =9 x 1 = 9
LCM(405,369) = ( 405 × 369 ) / 9
LCM(405,369) = 149445 / 9
LCM(405,369) = 16605
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FAQs on GCF of Fractions of 273/405, 506/369
1. What is the HCF of 273,506?
The HCF of 273,506 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 273/405, 506/369?
Answer: GCF of Numerators as per given numbers 273/405, 506/369 is
GCF of Numerators i.e. for 273,506 is 1
LCM of denominators i.e. for 405,369 is 16605.
Thus, GCF of Fractions is 1/16605.Finally, GCF of Fractions for 273/405, 506/369 is 1/16605.