GCF of 409/812, 129/422
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 409/812, 129/422 i.e 1/171332 easily. The following is the detailed procedure to determine the greatest common factor of fractions 409/812, 129/422.
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 409/812,129/422?
Given fractions are 409/812,129/422
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 409/812,129/422, numerators are 409,129
Denominators are 812,422
The GCF of 409,129 is 1 .
LCM of 812,422 is 171332.
The greatest common factor of 409/812,129/422 = [GCF of 409,129]/[LCM of 812,422]= 1/171332
Therefore, the GCF of 409/812,129/422 is 1/171332.
To find the highest common factor of 409,129, we have to find the factors of both numbers and list the highest common factor.
The factors of 409 are 1, 409
The factors of 129 are 1, 3, 43, 129
The HCF of 409,129 is 1.
Lets's calculate GCF of 409,129
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 409,129 By Matching Biggest Common Factor Method
Now, list down the factors of 409
:1,409
Now, list down the factors of 129
:1,3,43,129
Greatest Common Factor
We found the factors 409,129 . The biggest common factor number is the GCF number.
So the greatest common factor 409,129 is 1.
Lets's calculate LCM of 812,422
| 2 | 812, 422 |
| 406, 211 |
∴ So the LCM of the given numbers is 2 x 406 x 211 = 171332
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/171332
Therefore, the GCF of Fractions 409/812,129/422 is 1/171332
Least Common Multiple of 812,422 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 812,422 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(812,422) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(812,422) x common factors =2 x 1 = 2
LCM(812,422) = ( 812 × 422 ) / 2
LCM(812,422) = 342664 / 2
LCM(812,422) = 171332
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FAQs on GCF of Fractions of 409/812, 129/422
1. What is the HCF of 409,129?
The HCF of 409,129 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 409/812, 129/422?
Answer: GCF of Numerators as per given numbers 409/812, 129/422 is
GCF of Numerators i.e. for 409,129 is 1
LCM of denominators i.e. for 812,422 is 171332.
Thus, GCF of Fractions is 1/171332.Finally, GCF of Fractions for 409/812, 129/422 is 1/171332.