GCF of 206/75, 228/2913
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 206/75, 228/2913 i.e 2/72825 easily. The following is the detailed procedure to determine the greatest common factor of fractions 206/75, 228/2913.
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 206/75,228/2913?
Given fractions are 206/75,228/2913
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 206/75,228/2913, numerators are 206,228
Denominators are 75,2913
The GCF of 206,228 is 2 .
LCM of 75,2913 is 72825.
The greatest common factor of 206/75,228/2913 = [GCF of 206,228]/[LCM of 75,2913]= 2/72825
Therefore, the GCF of 206/75,228/2913 is 2/72825.
To find the highest common factor of 206,228, we have to find the factors of both numbers and list the highest common factor.
The factors of 206 are 1, 2, 103, 206
The factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
The HCF of 206,228 is 2.
Lets's calculate GCF of 206,228
| 2 | 206, 228 |
| 103, 114 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 206,228 By Matching Biggest Common Factor Method
Now, list down the factors of 206
:1,2,103,206
Now, list down the factors of 228
:1,2,3,4,6,12,19,38,57,76,114,228
Greatest Common Factor
We found the factors 206,228 . The biggest common factor number is the GCF number.
So the greatest common factor 206,228 is 2.
Lets's calculate LCM of 75,2913
| 3 | 75, 2913 |
| 25, 971 |
∴ So the LCM of the given numbers is 3 x 25 x 971 = 72825
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/72825
Therefore, the GCF of Fractions 206/75,228/2913 is 2/72825
Least Common Multiple of 75,2913 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 75,2913 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,2913) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(75,2913) x common factors =3 x 1 = 3
LCM(75,2913) = ( 75 × 2913 ) / 3
LCM(75,2913) = 218475 / 3
LCM(75,2913) = 72825
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FAQs on GCF of Fractions of 206/75, 228/2913
1. What is the HCF of 206,228?
The HCF of 206,228 is 2
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 206/75, 228/2913?
Answer: GCF of Numerators as per given numbers 206/75, 228/2913 is
GCF of Numerators i.e. for 206,228 is 2
LCM of denominators i.e. for 75,2913 is 72825.
Thus, GCF of Fractions is 2/72825.Finally, GCF of Fractions for 206/75, 228/2913 is 2/72825.