GCF of 8454/384, 8414/4592
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8454/384, 8414/4592 i.e 2/110208 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8454/384, 8414/4592.
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 8454/384,8414/4592?
Given fractions are 8454/384,8414/4592
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 8454/384,8414/4592, numerators are 8454,8414
Denominators are 384,4592
The GCF of 8454,8414 is 2 .
LCM of 384,4592 is 110208.
The greatest common factor of 8454/384,8414/4592 = [GCF of 8454,8414]/[LCM of 384,4592]= 2/110208
Therefore, the GCF of 8454/384,8414/4592 is 2/110208.
To find the highest common factor of 8454,8414, we have to find the factors of both numbers and list the highest common factor.
The factors of 8454 are 1, 2, 3, 6, 1409, 2818, 4227, 8454
The factors of 8414 are 1, 2, 7, 14, 601, 1202, 4207, 8414
The HCF of 8454,8414 is 2.
Lets's calculate GCF of 8454,8414
| 2 | 8454, 8414 |
| 4227, 4207 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8454,8414 By Matching Biggest Common Factor Method
Now, list down the factors of 8454
:1,2,3,6,1409,2818,4227,8454
Now, list down the factors of 8414
:1,2,7,14,601,1202,4207,8414
Greatest Common Factor
We found the factors 8454,8414 . The biggest common factor number is the GCF number.
So the greatest common factor 8454,8414 is 2.
Lets's calculate LCM of 384,4592
| 2 | 384, 4592 |
| 2 | 192, 2296 |
| 2 | 96, 1148 |
| 2 | 48, 574 |
| 24, 287 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 24 x 287 = 110208
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/110208
Therefore, the GCF of Fractions 8454/384,8414/4592 is 2/110208
Least Common Multiple of 384,4592 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 384,4592 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(384,4592) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(384,4592) x common factors =16 x 1 = 16
LCM(384,4592) = ( 384 × 4592 ) / 16
LCM(384,4592) = 1763328 / 16
LCM(384,4592) = 110208
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FAQs on GCF of Fractions of 8454/384, 8414/4592
1. What is the HCF of 8454,8414?
The HCF of 8454,8414 is 2
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 8454/384, 8414/4592?
Answer: GCF of Numerators as per given numbers 8454/384, 8414/4592 is
GCF of Numerators i.e. for 8454,8414 is 2
LCM of denominators i.e. for 384,4592 is 110208.
Thus, GCF of Fractions is 2/110208.Finally, GCF of Fractions for 8454/384, 8414/4592 is 2/110208.