GCF of 162/514, 462/404
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 162/514, 462/404 i.e 6/103828 easily. The following is the detailed procedure to determine the greatest common factor of fractions 162/514, 462/404.
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 162/514,462/404?
Given fractions are 162/514,462/404
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 162/514,462/404, numerators are 162,462
Denominators are 514,404
The GCF of 162,462 is 6 .
LCM of 514,404 is 103828.
The greatest common factor of 162/514,462/404 = [GCF of 162,462]/[LCM of 514,404]= 6/103828
Therefore, the GCF of 162/514,462/404 is 6/103828.
To find the highest common factor of 162,462, we have to find the factors of both numbers and list the highest common factor.
The factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81, 162
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The HCF of 162,462 is 6.
Lets's calculate GCF of 162,462
| 2 | 162, 462 |
| 3 | 81, 231 |
| 27, 77 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 162,462 By Matching Biggest Common Factor Method
Now, list down the factors of 162
:1,2,3,6,9,18,27,54,81,162
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Greatest Common Factor
We found the factors 162,462 . The biggest common factor number is the GCF number.
So the greatest common factor 162,462 is 6.
Lets's calculate LCM of 514,404
| 2 | 514, 404 |
| 257, 202 |
∴ So the LCM of the given numbers is 2 x 257 x 202 = 103828
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/103828
Therefore, the GCF of Fractions 162/514,462/404 is 6/103828
Least Common Multiple of 514,404 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 514,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(514,404) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(514,404) x common factors =2 x 1 = 2
LCM(514,404) = ( 514 × 404 ) / 2
LCM(514,404) = 207656 / 2
LCM(514,404) = 103828
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FAQs on GCF of Fractions of 162/514, 462/404
1. What is the HCF of 162,462?
The HCF of 162,462 is 6
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 162/514, 462/404?
Answer: GCF of Numerators as per given numbers 162/514, 462/404 is
GCF of Numerators i.e. for 162,462 is 6
LCM of denominators i.e. for 514,404 is 103828.
Thus, GCF of Fractions is 6/103828.Finally, GCF of Fractions for 162/514, 462/404 is 6/103828.