GCF of 204/275, 8454/209
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 204/275, 8454/209 i.e 6/5225 easily. The following is the detailed procedure to determine the greatest common factor of fractions 204/275, 8454/209.
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 204/275,8454/209?
Given fractions are 204/275,8454/209
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 204/275,8454/209, numerators are 204,8454
Denominators are 275,209
The GCF of 204,8454 is 6 .
LCM of 275,209 is 5225.
The greatest common factor of 204/275,8454/209 = [GCF of 204,8454]/[LCM of 275,209]= 6/5225
Therefore, the GCF of 204/275,8454/209 is 6/5225.
To find the highest common factor of 204,8454, we have to find the factors of both numbers and list the highest common factor.
The factors of 204 are 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204
The factors of 8454 are 1, 2, 3, 6, 1409, 2818, 4227, 8454
The HCF of 204,8454 is 6.
Lets's calculate GCF of 204,8454
| 2 | 204, 8454 |
| 3 | 102, 4227 |
| 34, 1409 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 204,8454 By Matching Biggest Common Factor Method
Now, list down the factors of 204
:1,2,3,4,6,12,17,34,51,68,102,204
Now, list down the factors of 8454
:1,2,3,6,1409,2818,4227,8454
Greatest Common Factor
We found the factors 204,8454 . The biggest common factor number is the GCF number.
So the greatest common factor 204,8454 is 6.
Lets's calculate LCM of 275,209
| 11 | 275, 209 |
| 25, 19 |
∴ So the LCM of the given numbers is 11 x 25 x 19 = 5225
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/5225
Therefore, the GCF of Fractions 204/275,8454/209 is 6/5225
Least Common Multiple of 275,209 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 275,209 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(275,209) = 11
common factors(in case of two or more numbers have common factors) = 1
GCF(275,209) x common factors =11 x 1 = 11
LCM(275,209) = ( 275 × 209 ) / 11
LCM(275,209) = 57475 / 11
LCM(275,209) = 5225
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 204/275, 8454/209
1. What is the HCF of 204,8454?
The HCF of 204,8454 is 6
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 204/275, 8454/209?
Answer: GCF of Numerators as per given numbers 204/275, 8454/209 is
GCF of Numerators i.e. for 204,8454 is 6
LCM of denominators i.e. for 275,209 is 5225.
Thus, GCF of Fractions is 6/5225.Finally, GCF of Fractions for 204/275, 8454/209 is 6/5225.