GCF of 1431/324, 2132/1238
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1431/324, 2132/1238 i.e 1/200556 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1431/324, 2132/1238.
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 1431/324,2132/1238?
Given fractions are 1431/324,2132/1238
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 1431/324,2132/1238, numerators are 1431,2132
Denominators are 324,1238
The GCF of 1431,2132 is 1 .
LCM of 324,1238 is 200556.
The greatest common factor of 1431/324,2132/1238 = [GCF of 1431,2132]/[LCM of 324,1238]= 1/200556
Therefore, the GCF of 1431/324,2132/1238 is 1/200556.
To find the highest common factor of 1431,2132, we have to find the factors of both numbers and list the highest common factor.
The factors of 1431 are 1, 3, 9, 27, 53, 159, 477, 1431
The factors of 2132 are 1, 2, 4, 13, 26, 41, 52, 82, 164, 533, 1066, 2132
The HCF of 1431,2132 is 1.
Lets's calculate GCF of 1431,2132
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1431,2132 By Matching Biggest Common Factor Method
Now, list down the factors of 1431
:1,3,9,27,53,159,477,1431
Now, list down the factors of 2132
:1,2,4,13,26,41,52,82,164,533,1066,2132
Greatest Common Factor
We found the factors 1431,2132 . The biggest common factor number is the GCF number.
So the greatest common factor 1431,2132 is 1.
Lets's calculate LCM of 324,1238
| 2 | 324, 1238 |
| 162, 619 |
∴ So the LCM of the given numbers is 2 x 162 x 619 = 200556
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/200556
Therefore, the GCF of Fractions 1431/324,2132/1238 is 1/200556
Least Common Multiple of 324,1238 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 324,1238 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(324,1238) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(324,1238) x common factors =2 x 1 = 2
LCM(324,1238) = ( 324 × 1238 ) / 2
LCM(324,1238) = 401112 / 2
LCM(324,1238) = 200556
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FAQs on GCF of Fractions of 1431/324, 2132/1238
1. What is the HCF of 1431,2132?
The HCF of 1431,2132 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 1431/324, 2132/1238?
Answer: GCF of Numerators as per given numbers 1431/324, 2132/1238 is
GCF of Numerators i.e. for 1431,2132 is 1
LCM of denominators i.e. for 324,1238 is 200556.
Thus, GCF of Fractions is 1/200556.Finally, GCF of Fractions for 1431/324, 2132/1238 is 1/200556.