GCF of 486/728, 837/394
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 486/728, 837/394 i.e 27/143416 easily. The following is the detailed procedure to determine the greatest common factor of fractions 486/728, 837/394.
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 486/728,837/394?
Given fractions are 486/728,837/394
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 486/728,837/394, numerators are 486,837
Denominators are 728,394
The GCF of 486,837 is 27 .
LCM of 728,394 is 143416.
The greatest common factor of 486/728,837/394 = [GCF of 486,837]/[LCM of 728,394]= 27/143416
Therefore, the GCF of 486/728,837/394 is 27/143416.
To find the highest common factor of 486,837, we have to find the factors of both numbers and list the highest common factor.
The factors of 486 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162, 243, 486
The factors of 837 are 1, 3, 9, 27, 31, 93, 279, 837
The HCF of 486,837 is 27.
Lets's calculate GCF of 486,837
| 3 | 486, 837 |
| 3 | 162, 279 |
| 3 | 54, 93 |
| 18, 31 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 486,837 By Matching Biggest Common Factor Method
Now, list down the factors of 486
:1,2,3,6,9,18,27,54,81,162,243,486
Now, list down the factors of 837
:1,3,9,27,31,93,279,837
Greatest Common Factor
We found the factors 486,837 . The biggest common factor number is the GCF number.
So the greatest common factor 486,837 is 27.
Lets's calculate LCM of 728,394
| 2 | 728, 394 |
| 364, 197 |
∴ So the LCM of the given numbers is 2 x 364 x 197 = 143416
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/143416
Therefore, the GCF of Fractions 486/728,837/394 is 27/143416
Least Common Multiple of 728,394 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 728,394 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(728,394) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(728,394) x common factors =2 x 1 = 2
LCM(728,394) = ( 728 × 394 ) / 2
LCM(728,394) = 286832 / 2
LCM(728,394) = 143416
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FAQs on GCF of Fractions of 486/728, 837/394
1. What is the HCF of 486,837?
The HCF of 486,837 is 27
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 486/728, 837/394?
Answer: GCF of Numerators as per given numbers 486/728, 837/394 is
GCF of Numerators i.e. for 486,837 is 27
LCM of denominators i.e. for 728,394 is 143416.
Thus, GCF of Fractions is 27/143416.Finally, GCF of Fractions for 486/728, 837/394 is 27/143416.