GCF of 396/161, 414/521
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 396/161, 414/521 i.e 18/83881 easily. The following is the detailed procedure to determine the greatest common factor of fractions 396/161, 414/521.
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 396/161,414/521?
Given fractions are 396/161,414/521
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 396/161,414/521, numerators are 396,414
Denominators are 161,521
The GCF of 396,414 is 18 .
LCM of 161,521 is 83881.
The greatest common factor of 396/161,414/521 = [GCF of 396,414]/[LCM of 161,521]= 18/83881
Therefore, the GCF of 396/161,414/521 is 18/83881.
To find the highest common factor of 396,414, we have to find the factors of both numbers and list the highest common factor.
The factors of 396 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The HCF of 396,414 is 18.
Lets's calculate GCF of 396,414
| 2 | 396, 414 |
| 3 | 198, 207 |
| 3 | 66, 69 |
| 22, 23 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 396,414 By Matching Biggest Common Factor Method
Now, list down the factors of 396
:1,2,3,4,6,9,11,12,18,22,33,36,44,66,99,132,198,396
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Greatest Common Factor
We found the factors 396,414 . The biggest common factor number is the GCF number.
So the greatest common factor 396,414 is 18.
Lets's calculate LCM of 161,521
Given numbers has no common factors except 1. So, there LCM is their product i.e 83881
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/83881
Therefore, the GCF of Fractions 396/161,414/521 is 18/83881
Least Common Multiple of 161,521 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 161,521 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(161,521) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(161,521) x common factors =1 x 1 = 1
LCM(161,521) = ( 161 × 521 ) / 1
LCM(161,521) = 83881 / 1
LCM(161,521) = 83881
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FAQs on GCF of Fractions of 396/161, 414/521
1. What is the HCF of 396,414?
The HCF of 396,414 is 18
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 396/161, 414/521?
Answer: GCF of Numerators as per given numbers 396/161, 414/521 is
GCF of Numerators i.e. for 396,414 is 18
LCM of denominators i.e. for 161,521 is 83881.
Thus, GCF of Fractions is 18/83881.Finally, GCF of Fractions for 396/161, 414/521 is 18/83881.