GCF of 465/866, 1271/198
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 465/866, 1271/198 i.e 31/85734 easily. The following is the detailed procedure to determine the greatest common factor of fractions 465/866, 1271/198.
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 465/866,1271/198?
Given fractions are 465/866,1271/198
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 465/866,1271/198, numerators are 465,1271
Denominators are 866,198
The GCF of 465,1271 is 31 .
LCM of 866,198 is 85734.
The greatest common factor of 465/866,1271/198 = [GCF of 465,1271]/[LCM of 866,198]= 31/85734
Therefore, the GCF of 465/866,1271/198 is 31/85734.
To find the highest common factor of 465,1271, we have to find the factors of both numbers and list the highest common factor.
The factors of 465 are 1, 3, 5, 15, 31, 93, 155, 465
The factors of 1271 are 1, 31, 41, 1271
The HCF of 465,1271 is 31.
Lets's calculate GCF of 465,1271
| 31 | 465, 1271 |
| 15, 41 |
∴ So the GCF of the given numbers is 31 = 31
Greatest Common Factor of 465,1271 By Matching Biggest Common Factor Method
Now, list down the factors of 465
:1,3,5,15,31,93,155,465
Now, list down the factors of 1271
:1,31,41,1271
Greatest Common Factor
We found the factors 465,1271 . The biggest common factor number is the GCF number.
So the greatest common factor 465,1271 is 31.
Lets's calculate LCM of 866,198
| 2 | 866, 198 |
| 433, 99 |
∴ So the LCM of the given numbers is 2 x 433 x 99 = 85734
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 31/85734
Therefore, the GCF of Fractions 465/866,1271/198 is 31/85734
Least Common Multiple of 866,198 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 866,198 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(866,198) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(866,198) x common factors =2 x 1 = 2
LCM(866,198) = ( 866 × 198 ) / 2
LCM(866,198) = 171468 / 2
LCM(866,198) = 85734
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FAQs on GCF of Fractions of 465/866, 1271/198
1. What is the HCF of 465,1271?
The HCF of 465,1271 is 31
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 465/866, 1271/198?
Answer: GCF of Numerators as per given numbers 465/866, 1271/198 is
GCF of Numerators i.e. for 465,1271 is 31
LCM of denominators i.e. for 866,198 is 85734.
Thus, GCF of Fractions is 31/85734.Finally, GCF of Fractions for 465/866, 1271/198 is 31/85734.