GCF of 591/582, 429/412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 591/582, 429/412 i.e 3/119892 easily. The following is the detailed procedure to determine the greatest common factor of fractions 591/582, 429/412.
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 591/582,429/412?
Given fractions are 591/582,429/412
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 591/582,429/412, numerators are 591,429
Denominators are 582,412
The GCF of 591,429 is 3 .
LCM of 582,412 is 119892.
The greatest common factor of 591/582,429/412 = [GCF of 591,429]/[LCM of 582,412]= 3/119892
Therefore, the GCF of 591/582,429/412 is 3/119892.
To find the highest common factor of 591,429, we have to find the factors of both numbers and list the highest common factor.
The factors of 591 are 1, 3, 197, 591
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The HCF of 591,429 is 3.
Lets's calculate GCF of 591,429
| 3 | 591, 429 |
| 197, 143 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 591,429 By Matching Biggest Common Factor Method
Now, list down the factors of 591
:1,3,197,591
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Greatest Common Factor
We found the factors 591,429 . The biggest common factor number is the GCF number.
So the greatest common factor 591,429 is 3.
Lets's calculate LCM of 582,412
| 2 | 582, 412 |
| 291, 206 |
∴ So the LCM of the given numbers is 2 x 291 x 206 = 119892
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/119892
Therefore, the GCF of Fractions 591/582,429/412 is 3/119892
Least Common Multiple of 582,412 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 582,412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(582,412) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(582,412) x common factors =2 x 1 = 2
LCM(582,412) = ( 582 × 412 ) / 2
LCM(582,412) = 239784 / 2
LCM(582,412) = 119892
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FAQs on GCF of Fractions of 591/582, 429/412
1. What is the HCF of 591,429?
The HCF of 591,429 is 3
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 591/582, 429/412?
Answer: GCF of Numerators as per given numbers 591/582, 429/412 is
GCF of Numerators i.e. for 591,429 is 3
LCM of denominators i.e. for 582,412 is 119892.
Thus, GCF of Fractions is 3/119892.Finally, GCF of Fractions for 591/582, 429/412 is 3/119892.