GCF of 431/364, 289/398
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 431/364, 289/398 i.e 1/72436 easily. The following is the detailed procedure to determine the greatest common factor of fractions 431/364, 289/398.
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 431/364,289/398?
Given fractions are 431/364,289/398
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 431/364,289/398, numerators are 431,289
Denominators are 364,398
The GCF of 431,289 is 1 .
LCM of 364,398 is 72436.
The greatest common factor of 431/364,289/398 = [GCF of 431,289]/[LCM of 364,398]= 1/72436
Therefore, the GCF of 431/364,289/398 is 1/72436.
To find the highest common factor of 431,289, we have to find the factors of both numbers and list the highest common factor.
The factors of 431 are 1, 431
The factors of 289 are 1, 17, 289
The HCF of 431,289 is 1.
Lets's calculate GCF of 431,289
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 431,289 By Matching Biggest Common Factor Method
Now, list down the factors of 431
:1,431
Now, list down the factors of 289
:1,17,289
Greatest Common Factor
We found the factors 431,289 . The biggest common factor number is the GCF number.
So the greatest common factor 431,289 is 1.
Lets's calculate LCM of 364,398
| 2 | 364, 398 |
| 182, 199 |
∴ So the LCM of the given numbers is 2 x 182 x 199 = 72436
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/72436
Therefore, the GCF of Fractions 431/364,289/398 is 1/72436
Least Common Multiple of 364,398 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 364,398 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(364,398) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(364,398) x common factors =2 x 1 = 2
LCM(364,398) = ( 364 × 398 ) / 2
LCM(364,398) = 144872 / 2
LCM(364,398) = 72436
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 431/364, 289/398
1. What is the HCF of 431,289?
The HCF of 431,289 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 431/364, 289/398?
Answer: GCF of Numerators as per given numbers 431/364, 289/398 is
GCF of Numerators i.e. for 431,289 is 1
LCM of denominators i.e. for 364,398 is 72436.
Thus, GCF of Fractions is 1/72436.Finally, GCF of Fractions for 431/364, 289/398 is 1/72436.