GCF of 209/115, 314/885
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 209/115, 314/885 i.e 1/20355 easily. The following is the detailed procedure to determine the greatest common factor of fractions 209/115, 314/885.
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 209/115,314/885?
Given fractions are 209/115,314/885
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 209/115,314/885, numerators are 209,314
Denominators are 115,885
The GCF of 209,314 is 1 .
LCM of 115,885 is 20355.
The greatest common factor of 209/115,314/885 = [GCF of 209,314]/[LCM of 115,885]= 1/20355
Therefore, the GCF of 209/115,314/885 is 1/20355.
To find the highest common factor of 209,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 209 are 1, 11, 19, 209
The factors of 314 are 1, 2, 157, 314
The HCF of 209,314 is 1.
Lets's calculate GCF of 209,314
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 209,314 By Matching Biggest Common Factor Method
Now, list down the factors of 209
:1,11,19,209
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 209,314 . The biggest common factor number is the GCF number.
So the greatest common factor 209,314 is 1.
Lets's calculate LCM of 115,885
| 5 | 115, 885 |
| 23, 177 |
∴ So the LCM of the given numbers is 5 x 23 x 177 = 20355
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/20355
Therefore, the GCF of Fractions 209/115,314/885 is 1/20355
Least Common Multiple of 115,885 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 115,885 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(115,885) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(115,885) x common factors =5 x 1 = 5
LCM(115,885) = ( 115 × 885 ) / 5
LCM(115,885) = 101775 / 5
LCM(115,885) = 20355
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FAQs on GCF of Fractions of 209/115, 314/885
1. What is the HCF of 209,314?
The HCF of 209,314 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 209/115, 314/885?
Answer: GCF of Numerators as per given numbers 209/115, 314/885 is
GCF of Numerators i.e. for 209,314 is 1
LCM of denominators i.e. for 115,885 is 20355.
Thus, GCF of Fractions is 1/20355.Finally, GCF of Fractions for 209/115, 314/885 is 1/20355.