GCF of 231/74, 319/205
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 231/74, 319/205 i.e 11/15170 easily. The following is the detailed procedure to determine the greatest common factor of fractions 231/74, 319/205.
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 231/74,319/205?
Given fractions are 231/74,319/205
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 231/74,319/205, numerators are 231,319
Denominators are 74,205
The GCF of 231,319 is 11 .
LCM of 74,205 is 15170.
The greatest common factor of 231/74,319/205 = [GCF of 231,319]/[LCM of 74,205]= 11/15170
Therefore, the GCF of 231/74,319/205 is 11/15170.
To find the highest common factor of 231,319, we have to find the factors of both numbers and list the highest common factor.
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The factors of 319 are 1, 11, 29, 319
The HCF of 231,319 is 11.
Lets's calculate GCF of 231,319
| 11 | 231, 319 |
| 21, 29 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 231,319 By Matching Biggest Common Factor Method
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Now, list down the factors of 319
:1,11,29,319
Greatest Common Factor
We found the factors 231,319 . The biggest common factor number is the GCF number.
So the greatest common factor 231,319 is 11.
Lets's calculate LCM of 74,205
Given numbers has no common factors except 1. So, there LCM is their product i.e 15170
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/15170
Therefore, the GCF of Fractions 231/74,319/205 is 11/15170
Least Common Multiple of 74,205 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 74,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,205) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(74,205) x common factors =1 x 1 = 1
LCM(74,205) = ( 74 × 205 ) / 1
LCM(74,205) = 15170 / 1
LCM(74,205) = 15170
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FAQs on GCF of Fractions of 231/74, 319/205
1. What is the HCF of 231,319?
The HCF of 231,319 is 11
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 231/74, 319/205?
Answer: GCF of Numerators as per given numbers 231/74, 319/205 is
GCF of Numerators i.e. for 231,319 is 11
LCM of denominators i.e. for 74,205 is 15170.
Thus, GCF of Fractions is 11/15170.Finally, GCF of Fractions for 231/74, 319/205 is 11/15170.