GCF of 474/109, 462/129
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 474/109, 462/129 i.e 6/14061 easily. The following is the detailed procedure to determine the greatest common factor of fractions 474/109, 462/129.
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 474/109,462/129?
Given fractions are 474/109,462/129
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 474/109,462/129, numerators are 474,462
Denominators are 109,129
The GCF of 474,462 is 6 .
LCM of 109,129 is 14061.
The greatest common factor of 474/109,462/129 = [GCF of 474,462]/[LCM of 109,129]= 6/14061
Therefore, the GCF of 474/109,462/129 is 6/14061.
To find the highest common factor of 474,462, we have to find the factors of both numbers and list the highest common factor.
The factors of 474 are 1, 2, 3, 6, 79, 158, 237, 474
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The HCF of 474,462 is 6.
Lets's calculate GCF of 474,462
| 2 | 474, 462 |
| 3 | 237, 231 |
| 79, 77 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 474,462 By Matching Biggest Common Factor Method
Now, list down the factors of 474
:1,2,3,6,79,158,237,474
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 474,462 . The biggest common factor number is the GCF number.
So the greatest common factor 474,462 is 6.
Lets's calculate LCM of 109,129
Given numbers has no common factors except 1. So, there LCM is their product i.e 14061
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/14061
Therefore, the GCF of Fractions 474/109,462/129 is 6/14061
Least Common Multiple of 109,129 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 109,129 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(109,129) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(109,129) x common factors =1 x 1 = 1
LCM(109,129) = ( 109 × 129 ) / 1
LCM(109,129) = 14061 / 1
LCM(109,129) = 14061
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FAQs on GCF of Fractions of 474/109, 462/129
1. What is the HCF of 474,462?
The HCF of 474,462 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 474/109, 462/129?
Answer: GCF of Numerators as per given numbers 474/109, 462/129 is
GCF of Numerators i.e. for 474,462 is 6
LCM of denominators i.e. for 109,129 is 14061.
Thus, GCF of Fractions is 6/14061.Finally, GCF of Fractions for 474/109, 462/129 is 6/14061.