GCF of 665/198, 705/293
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 665/198, 705/293 i.e 5/58014 easily. The following is the detailed procedure to determine the greatest common factor of fractions 665/198, 705/293.
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 665/198,705/293?
Given fractions are 665/198,705/293
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 665/198,705/293, numerators are 665,705
Denominators are 198,293
The GCF of 665,705 is 5 .
LCM of 198,293 is 58014.
The greatest common factor of 665/198,705/293 = [GCF of 665,705]/[LCM of 198,293]= 5/58014
Therefore, the GCF of 665/198,705/293 is 5/58014.
To find the highest common factor of 665,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 665 are 1, 5, 7, 19, 35, 95, 133, 665
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 665,705 is 5.
Lets's calculate GCF of 665,705
| 5 | 665, 705 |
| 133, 141 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 665,705 By Matching Biggest Common Factor Method
Now, list down the factors of 665
:1,5,7,19,35,95,133,665
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 665,705 . The biggest common factor number is the GCF number.
So the greatest common factor 665,705 is 5.
Lets's calculate LCM of 198,293
Given numbers has no common factors except 1. So, there LCM is their product i.e 58014
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/58014
Therefore, the GCF of Fractions 665/198,705/293 is 5/58014
Least Common Multiple of 198,293 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 198,293 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(198,293) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(198,293) x common factors =1 x 1 = 1
LCM(198,293) = ( 198 × 293 ) / 1
LCM(198,293) = 58014 / 1
LCM(198,293) = 58014
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FAQs on GCF of Fractions of 665/198, 705/293
1. What is the HCF of 665,705?
The HCF of 665,705 is 5
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 665/198, 705/293?
Answer: GCF of Numerators as per given numbers 665/198, 705/293 is
GCF of Numerators i.e. for 665,705 is 5
LCM of denominators i.e. for 198,293 is 58014.
Thus, GCF of Fractions is 5/58014.Finally, GCF of Fractions for 665/198, 705/293 is 5/58014.