GCF of 223/416, 1909/242
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 223/416, 1909/242 i.e 1/50336 easily. The following is the detailed procedure to determine the greatest common factor of fractions 223/416, 1909/242.
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 223/416,1909/242?
Given fractions are 223/416,1909/242
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 223/416,1909/242, numerators are 223,1909
Denominators are 416,242
The GCF of 223,1909 is 1 .
LCM of 416,242 is 50336.
The greatest common factor of 223/416,1909/242 = [GCF of 223,1909]/[LCM of 416,242]= 1/50336
Therefore, the GCF of 223/416,1909/242 is 1/50336.
To find the highest common factor of 223,1909, we have to find the factors of both numbers and list the highest common factor.
The factors of 223 are 1, 223
The factors of 1909 are 1, 23, 83, 1909
The HCF of 223,1909 is 1.
Lets's calculate GCF of 223,1909
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 223,1909 By Matching Biggest Common Factor Method
Now, list down the factors of 223
:1,223
Now, list down the factors of 1909
:1,23,83,1909
Greatest Common Factor
We found the factors 223,1909 . The biggest common factor number is the GCF number.
So the greatest common factor 223,1909 is 1.
Lets's calculate LCM of 416,242
| 2 | 416, 242 |
| 208, 121 |
∴ So the LCM of the given numbers is 2 x 208 x 121 = 50336
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/50336
Therefore, the GCF of Fractions 223/416,1909/242 is 1/50336
Least Common Multiple of 416,242 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 416,242 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(416,242) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(416,242) x common factors =2 x 1 = 2
LCM(416,242) = ( 416 × 242 ) / 2
LCM(416,242) = 100672 / 2
LCM(416,242) = 50336
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FAQs on GCF of Fractions of 223/416, 1909/242
1. What is the HCF of 223,1909?
The HCF of 223,1909 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 223/416, 1909/242?
Answer: GCF of Numerators as per given numbers 223/416, 1909/242 is
GCF of Numerators i.e. for 223,1909 is 1
LCM of denominators i.e. for 416,242 is 50336.
Thus, GCF of Fractions is 1/50336.Finally, GCF of Fractions for 223/416, 1909/242 is 1/50336.