GCF of 273/212, 585/390
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 273/212, 585/390 i.e 39/41340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 273/212, 585/390.
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 273/212,585/390?
Given fractions are 273/212,585/390
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 273/212,585/390, numerators are 273,585
Denominators are 212,390
The GCF of 273,585 is 39 .
LCM of 212,390 is 41340.
The greatest common factor of 273/212,585/390 = [GCF of 273,585]/[LCM of 212,390]= 39/41340
Therefore, the GCF of 273/212,585/390 is 39/41340.
To find the highest common factor of 273,585, 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 585 are 1, 3, 5, 9, 13, 15, 39, 45, 65, 117, 195, 585
The HCF of 273,585 is 39.
Lets's calculate GCF of 273,585
| 3 | 273, 585 |
| 13 | 91, 195 |
| 7, 15 |
∴ So the GCF of the given numbers is 3 x 13 = 39
Greatest Common Factor of 273,585 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 585
:1,3,5,9,13,15,39,45,65,117,195,585
Greatest Common Factor
We found the factors 273,585 . The biggest common factor number is the GCF number.
So the greatest common factor 273,585 is 39.
Lets's calculate LCM of 212,390
| 2 | 212, 390 |
| 106, 195 |
∴ So the LCM of the given numbers is 2 x 106 x 195 = 41340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 39/41340
Therefore, the GCF of Fractions 273/212,585/390 is 39/41340
Least Common Multiple of 212,390 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 212,390 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(212,390) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(212,390) x common factors =2 x 1 = 2
LCM(212,390) = ( 212 × 390 ) / 2
LCM(212,390) = 82680 / 2
LCM(212,390) = 41340
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FAQs on GCF of Fractions of 273/212, 585/390
1. What is the HCF of 273,585?
The HCF of 273,585 is 39
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 273/212, 585/390?
Answer: GCF of Numerators as per given numbers 273/212, 585/390 is
GCF of Numerators i.e. for 273,585 is 39
LCM of denominators i.e. for 212,390 is 41340.
Thus, GCF of Fractions is 39/41340.Finally, GCF of Fractions for 273/212, 585/390 is 39/41340.