GCF of 8082/287, 8784/2267
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8082/287, 8784/2267 i.e 18/650629 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8082/287, 8784/2267.
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 8082/287,8784/2267?
Given fractions are 8082/287,8784/2267
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 8082/287,8784/2267, numerators are 8082,8784
Denominators are 287,2267
The GCF of 8082,8784 is 18 .
LCM of 287,2267 is 650629.
The greatest common factor of 8082/287,8784/2267 = [GCF of 8082,8784]/[LCM of 287,2267]= 18/650629
Therefore, the GCF of 8082/287,8784/2267 is 18/650629.
To find the highest common factor of 8082,8784, 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 8784 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 61, 72, 122, 144, 183, 244, 366, 488, 549, 732, 976, 1098, 1464, 2196, 2928, 4392, 8784
The HCF of 8082,8784 is 18.
Lets's calculate GCF of 8082,8784
| 2 | 8082, 8784 |
| 3 | 4041, 4392 |
| 3 | 1347, 1464 |
| 449, 488 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 8082,8784 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 8784
:1,2,3,4,6,8,9,12,16,18,24,36,48,61,72,122,144,183,244,366,488,549,732,976,1098,1464,2196,2928,4392,8784
Greatest Common Factor
We found the factors 8082,8784 . The biggest common factor number is the GCF number.
So the greatest common factor 8082,8784 is 18.
Lets's calculate LCM of 287,2267
Given numbers has no common factors except 1. So, there LCM is their product i.e 650629
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/650629
Therefore, the GCF of Fractions 8082/287,8784/2267 is 18/650629
Least Common Multiple of 287,2267 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 287,2267 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(287,2267) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(287,2267) x common factors =1 x 1 = 1
LCM(287,2267) = ( 287 × 2267 ) / 1
LCM(287,2267) = 650629 / 1
LCM(287,2267) = 650629
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FAQs on GCF of Fractions of 8082/287, 8784/2267
1. What is the HCF of 8082,8784?
The HCF of 8082,8784 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 8082/287, 8784/2267?
Answer: GCF of Numerators as per given numbers 8082/287, 8784/2267 is
GCF of Numerators i.e. for 8082,8784 is 18
LCM of denominators i.e. for 287,2267 is 650629.
Thus, GCF of Fractions is 18/650629.Finally, GCF of Fractions for 8082/287, 8784/2267 is 18/650629.