GCF of 8082/331, 8184/203
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8082/331, 8184/203 i.e 6/67193 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8082/331, 8184/203.
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 8082/331,8184/203?
Given fractions are 8082/331,8184/203
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 8082/331,8184/203, numerators are 8082,8184
Denominators are 331,203
The GCF of 8082,8184 is 6 .
LCM of 331,203 is 67193.
The greatest common factor of 8082/331,8184/203 = [GCF of 8082,8184]/[LCM of 331,203]= 6/67193
Therefore, the GCF of 8082/331,8184/203 is 6/67193.
To find the highest common factor of 8082,8184, we have to find the factors of both numbers and list the highest common factor.
The factors of 8082 are 1, 2, 3, 6, 9, 18, 449, 898, 1347, 2694, 4041, 8082
The factors of 8184 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 31, 33, 44, 62, 66, 88, 93, 124, 132, 186, 248, 264, 341, 372, 682, 744, 1023, 1364, 2046, 2728, 4092, 8184
The HCF of 8082,8184 is 6.
Lets's calculate GCF of 8082,8184
| 2 | 8082, 8184 |
| 3 | 4041, 4092 |
| 1347, 1364 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 8082,8184 By Matching Biggest Common Factor Method
Now, list down the factors of 8082
:1,2,3,6,9,18,449,898,1347,2694,4041,8082
Now, list down the factors of 8184
:1,2,3,4,6,8,11,12,22,24,31,33,44,62,66,88,93,124,132,186,248,264,341,372,682,744,1023,1364,2046,2728,4092,8184
Greatest Common Factor
We found the factors 8082,8184 . The biggest common factor number is the GCF number.
So the greatest common factor 8082,8184 is 6.
Lets's calculate LCM of 331,203
Given numbers has no common factors except 1. So, there LCM is their product i.e 67193
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/67193
Therefore, the GCF of Fractions 8082/331,8184/203 is 6/67193
Least Common Multiple of 331,203 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 331,203 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(331,203) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(331,203) x common factors =1 x 1 = 1
LCM(331,203) = ( 331 × 203 ) / 1
LCM(331,203) = 67193 / 1
LCM(331,203) = 67193
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FAQs on GCF of Fractions of 8082/331, 8184/203
1. What is the HCF of 8082,8184?
The HCF of 8082,8184 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 8082/331, 8184/203?
Answer: GCF of Numerators as per given numbers 8082/331, 8184/203 is
GCF of Numerators i.e. for 8082,8184 is 6
LCM of denominators i.e. for 331,203 is 67193.
Thus, GCF of Fractions is 6/67193.Finally, GCF of Fractions for 8082/331, 8184/203 is 6/67193.