GCF of 330/31, 231/257
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 330/31, 231/257 i.e 33/7967 easily. The following is the detailed procedure to determine the greatest common factor of fractions 330/31, 231/257.
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 330/31,231/257?
Given fractions are 330/31,231/257
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 330/31,231/257, numerators are 330,231
Denominators are 31,257
The GCF of 330,231 is 33 .
LCM of 31,257 is 7967.
The greatest common factor of 330/31,231/257 = [GCF of 330,231]/[LCM of 31,257]= 33/7967
Therefore, the GCF of 330/31,231/257 is 33/7967.
To find the highest common factor of 330,231, we have to find the factors of both numbers and list the highest common factor.
The factors of 330 are 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330
The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231
The HCF of 330,231 is 33.
Lets's calculate GCF of 330,231
| 3 | 330, 231 |
| 11 | 110, 77 |
| 10, 7 |
∴ So the GCF of the given numbers is 3 x 11 = 33
Greatest Common Factor of 330,231 By Matching Biggest Common Factor Method
Now, list down the factors of 330
:1,2,3,5,6,10,11,15,22,30,33,55,66,110,165,330
Now, list down the factors of 231
:1,3,7,11,21,33,77,231
Greatest Common Factor
We found the factors 330,231 . The biggest common factor number is the GCF number.
So the greatest common factor 330,231 is 33.
Lets's calculate LCM of 31,257
Given numbers has no common factors except 1. So, there LCM is their product i.e 7967
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 33/7967
Therefore, the GCF of Fractions 330/31,231/257 is 33/7967
Least Common Multiple of 31,257 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 31,257 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,257) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(31,257) x common factors =1 x 1 = 1
LCM(31,257) = ( 31 × 257 ) / 1
LCM(31,257) = 7967 / 1
LCM(31,257) = 7967
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FAQs on GCF of Fractions of 330/31, 231/257
1. What is the HCF of 330,231?
The HCF of 330,231 is 33
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 330/31, 231/257?
Answer: GCF of Numerators as per given numbers 330/31, 231/257 is
GCF of Numerators i.e. for 330,231 is 33
LCM of denominators i.e. for 31,257 is 7967.
Thus, GCF of Fractions is 33/7967.Finally, GCF of Fractions for 330/31, 231/257 is 33/7967.