GCF of 54/192, 69/449, 830/916
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 54/192, 69/449, 830/916 i.e 1/19741632 easily. The following is the detailed procedure to determine the greatest common factor of fractions 54/192, 69/449, 830/916.
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 54/192,69/449,830/916?
Given fractions are 54/192,69/449,830/916
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 54/192,69/449,830/916, numerators are 54,69,830
Denominators are 192,449,916
The GCF of 54,69,830 is 1 .
LCM of 192,449,916 is 19741632.
The greatest common factor of 54/192,69/449,830/916 = [GCF of 54,69,830]/[LCM of 192,449,916]= 1/19741632
Therefore, the GCF of 54/192,69/449,830/916 is 1/19741632.
To find the highest common factor of 54,69,830, we have to find the factors of both numbers and list the highest common factor.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
The factors of 69 are 1, 3, 23, 69
The factors of 830 are 1, 2, 5, 10, 83, 166, 415, 830
The HCF of 54,69,830 is 1.
Lets's calculate GCF of 54,69,830
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 54,69,830 By Matching Biggest Common Factor Method
Now, list down the factors of 54
:1,2,3,6,9,18,27,54
Now, list down the factors of 69
:1,3,23,69
Now, list down the factors of 830
:1,2,5,10,83,166,415,830
Greatest Common Factor
We found the factors 54,69,830 . The biggest common factor number is the GCF number.
So the greatest common factor 54,69,830 is 1.
Lets's calculate LCM of 192,449,916
| 2 | 192, 449, 916 |
| 2 | 96, 449, 458 |
| 48, 449, 229 |
∴ So the LCM of the given numbers is 2 x 2 x 48 x 449 x 229 = 19741632
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/19741632
Therefore, the GCF of Fractions 54/192,69/449,830/916 is 1/19741632
Least Common Multiple of 192,449,916 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 192,449,916 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(192,449,916) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(192,449,916) x common factors =1 x 4 = 4
LCM(192,449,916) = ( 192 × 449 × 916 ) / 4
LCM(192,449,916) = 78966528 / 4
LCM(192,449,916) = 19741632
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 54/192, 69/449, 830/916
1. What is the HCF of 54,69,830?
The HCF of 54,69,830 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 54/192, 69/449, 830/916?
Answer: GCF of Numerators as per given numbers 54/192, 69/449, 830/916 is
GCF of Numerators i.e. for 54,69,830 is 1
LCM of denominators i.e. for 192,449,916 is 19741632.
Thus, GCF of Fractions is 1/19741632.Finally, GCF of Fractions for 54/192, 69/449, 830/916 is 1/19741632.