GCF of 420/205, 238/195
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 420/205, 238/195 i.e 14/7995 easily. The following is the detailed procedure to determine the greatest common factor of fractions 420/205, 238/195.
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 420/205,238/195?
Given fractions are 420/205,238/195
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 420/205,238/195, numerators are 420,238
Denominators are 205,195
The GCF of 420,238 is 14 .
LCM of 205,195 is 7995.
The greatest common factor of 420/205,238/195 = [GCF of 420,238]/[LCM of 205,195]= 14/7995
Therefore, the GCF of 420/205,238/195 is 14/7995.
To find the highest common factor of 420,238, we have to find the factors of both numbers and list the highest common factor.
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The factors of 238 are 1, 2, 7, 14, 17, 34, 119, 238
The HCF of 420,238 is 14.
Lets's calculate GCF of 420,238
| 2 | 420, 238 |
| 7 | 210, 119 |
| 30, 17 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 420,238 By Matching Biggest Common Factor Method
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Now, list down the factors of 238
:1,2,7,14,17,34,119,238
Greatest Common Factor
We found the factors 420,238 . The biggest common factor number is the GCF number.
So the greatest common factor 420,238 is 14.
Lets's calculate LCM of 205,195
| 5 | 205, 195 |
| 41, 39 |
∴ So the LCM of the given numbers is 5 x 41 x 39 = 7995
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/7995
Therefore, the GCF of Fractions 420/205,238/195 is 14/7995
Least Common Multiple of 205,195 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 205,195 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,195) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(205,195) x common factors =5 x 1 = 5
LCM(205,195) = ( 205 × 195 ) / 5
LCM(205,195) = 39975 / 5
LCM(205,195) = 7995
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 420/205, 238/195
1. What is the HCF of 420,238?
The HCF of 420,238 is 14
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 420/205, 238/195?
Answer: GCF of Numerators as per given numbers 420/205, 238/195 is
GCF of Numerators i.e. for 420,238 is 14
LCM of denominators i.e. for 205,195 is 7995.
Thus, GCF of Fractions is 14/7995.Finally, GCF of Fractions for 420/205, 238/195 is 14/7995.