GCF of 257/82, 198/764
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 257/82, 198/764 i.e 1/31324 easily. The following is the detailed procedure to determine the greatest common factor of fractions 257/82, 198/764.
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 257/82,198/764?
Given fractions are 257/82,198/764
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 257/82,198/764, numerators are 257,198
Denominators are 82,764
The GCF of 257,198 is 1 .
LCM of 82,764 is 31324.
The greatest common factor of 257/82,198/764 = [GCF of 257,198]/[LCM of 82,764]= 1/31324
Therefore, the GCF of 257/82,198/764 is 1/31324.
To find the highest common factor of 257,198, we have to find the factors of both numbers and list the highest common factor.
The factors of 257 are 1, 257
The factors of 198 are 1, 2, 3, 6, 9, 11, 18, 22, 33, 66, 99, 198
The HCF of 257,198 is 1.
Lets's calculate GCF of 257,198
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 257,198 By Matching Biggest Common Factor Method
Now, list down the factors of 257
:1,257
Now, list down the factors of 198
:1,2,3,6,9,11,18,22,33,66,99,198
Greatest Common Factor
We found the factors 257,198 . The biggest common factor number is the GCF number.
So the greatest common factor 257,198 is 1.
Lets's calculate LCM of 82,764
| 2 | 82, 764 |
| 41, 382 |
∴ So the LCM of the given numbers is 2 x 41 x 382 = 31324
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31324
Therefore, the GCF of Fractions 257/82,198/764 is 1/31324
Least Common Multiple of 82,764 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 82,764 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(82,764) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(82,764) x common factors =2 x 1 = 2
LCM(82,764) = ( 82 × 764 ) / 2
LCM(82,764) = 62648 / 2
LCM(82,764) = 31324
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FAQs on GCF of Fractions of 257/82, 198/764
1. What is the HCF of 257,198?
The HCF of 257,198 is 1
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 257/82, 198/764?
Answer: GCF of Numerators as per given numbers 257/82, 198/764 is
GCF of Numerators i.e. for 257,198 is 1
LCM of denominators i.e. for 82,764 is 31324.
Thus, GCF of Fractions is 1/31324.Finally, GCF of Fractions for 257/82, 198/764 is 1/31324.