GCF of 319/18, 609/2198
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 319/18, 609/2198 i.e 29/19782 easily. The following is the detailed procedure to determine the greatest common factor of fractions 319/18, 609/2198.
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 319/18,609/2198?
Given fractions are 319/18,609/2198
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 319/18,609/2198, numerators are 319,609
Denominators are 18,2198
The GCF of 319,609 is 29 .
LCM of 18,2198 is 19782.
The greatest common factor of 319/18,609/2198 = [GCF of 319,609]/[LCM of 18,2198]= 29/19782
Therefore, the GCF of 319/18,609/2198 is 29/19782.
To find the highest common factor of 319,609, we have to find the factors of both numbers and list the highest common factor.
The factors of 319 are 1, 11, 29, 319
The factors of 609 are 1, 3, 7, 21, 29, 87, 203, 609
The HCF of 319,609 is 29.
Lets's calculate GCF of 319,609
| 29 | 319, 609 |
| 11, 21 |
∴ So the GCF of the given numbers is 29 = 29
Greatest Common Factor of 319,609 By Matching Biggest Common Factor Method
Now, list down the factors of 319
:1,11,29,319
Now, list down the factors of 609
:1,3,7,21,29,87,203,609
Greatest Common Factor
We found the factors 319,609 . The biggest common factor number is the GCF number.
So the greatest common factor 319,609 is 29.
Lets's calculate LCM of 18,2198
| 2 | 18, 2198 |
| 9, 1099 |
∴ So the LCM of the given numbers is 2 x 9 x 1099 = 19782
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 29/19782
Therefore, the GCF of Fractions 319/18,609/2198 is 29/19782
Least Common Multiple of 18,2198 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 18,2198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,2198) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(18,2198) x common factors =2 x 1 = 2
LCM(18,2198) = ( 18 × 2198 ) / 2
LCM(18,2198) = 39564 / 2
LCM(18,2198) = 19782
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FAQs on GCF of Fractions of 319/18, 609/2198
1. What is the HCF of 319,609?
The HCF of 319,609 is 29
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 319/18, 609/2198?
Answer: GCF of Numerators as per given numbers 319/18, 609/2198 is
GCF of Numerators i.e. for 319,609 is 29
LCM of denominators i.e. for 18,2198 is 19782.
Thus, GCF of Fractions is 29/19782.Finally, GCF of Fractions for 319/18, 609/2198 is 29/19782.