GCF of 405/74, 429/844
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 405/74, 429/844 i.e 3/31228 easily. The following is the detailed procedure to determine the greatest common factor of fractions 405/74, 429/844.
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 405/74,429/844?
Given fractions are 405/74,429/844
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 405/74,429/844, numerators are 405,429
Denominators are 74,844
The GCF of 405,429 is 3 .
LCM of 74,844 is 31228.
The greatest common factor of 405/74,429/844 = [GCF of 405,429]/[LCM of 74,844]= 3/31228
Therefore, the GCF of 405/74,429/844 is 3/31228.
To find the highest common factor of 405,429, we have to find the factors of both numbers and list the highest common factor.
The factors of 405 are 1, 3, 5, 9, 15, 27, 45, 81, 135, 405
The factors of 429 are 1, 3, 11, 13, 33, 39, 143, 429
The HCF of 405,429 is 3.
Lets's calculate GCF of 405,429
| 3 | 405, 429 |
| 135, 143 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 405,429 By Matching Biggest Common Factor Method
Now, list down the factors of 405
:1,3,5,9,15,27,45,81,135,405
Now, list down the factors of 429
:1,3,11,13,33,39,143,429
Greatest Common Factor
We found the factors 405,429 . The biggest common factor number is the GCF number.
So the greatest common factor 405,429 is 3.
Lets's calculate LCM of 74,844
| 2 | 74, 844 |
| 37, 422 |
∴ So the LCM of the given numbers is 2 x 37 x 422 = 31228
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/31228
Therefore, the GCF of Fractions 405/74,429/844 is 3/31228
Least Common Multiple of 74,844 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 74,844 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,844) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(74,844) x common factors =2 x 1 = 2
LCM(74,844) = ( 74 × 844 ) / 2
LCM(74,844) = 62456 / 2
LCM(74,844) = 31228
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FAQs on GCF of Fractions of 405/74, 429/844
1. What is the HCF of 405,429?
The HCF of 405,429 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 405/74, 429/844?
Answer: GCF of Numerators as per given numbers 405/74, 429/844 is
GCF of Numerators i.e. for 405,429 is 3
LCM of denominators i.e. for 74,844 is 31228.
Thus, GCF of Fractions is 3/31228.Finally, GCF of Fractions for 405/74, 429/844 is 3/31228.