GCF of 8082/731, 9829/7412
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8082/731, 9829/7412 i.e 1/318716 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8082/731, 9829/7412.
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 8082/731,9829/7412?
Given fractions are 8082/731,9829/7412
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 8082/731,9829/7412, numerators are 8082,9829
Denominators are 731,7412
The GCF of 8082,9829 is 1 .
LCM of 731,7412 is 318716.
The greatest common factor of 8082/731,9829/7412 = [GCF of 8082,9829]/[LCM of 731,7412]= 1/318716
Therefore, the GCF of 8082/731,9829/7412 is 1/318716.
To find the highest common factor of 8082,9829, 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 9829 are 1, 9829
The HCF of 8082,9829 is 1.
Lets's calculate GCF of 8082,9829
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8082,9829 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 9829
:1,9829
Greatest Common Factor
We found the factors 8082,9829 . The biggest common factor number is the GCF number.
So the greatest common factor 8082,9829 is 1.
Lets's calculate LCM of 731,7412
| 17 | 731, 7412 |
| 43, 436 |
∴ So the LCM of the given numbers is 17 x 43 x 436 = 318716
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/318716
Therefore, the GCF of Fractions 8082/731,9829/7412 is 1/318716
Least Common Multiple of 731,7412 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 731,7412 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(731,7412) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(731,7412) x common factors =17 x 1 = 17
LCM(731,7412) = ( 731 × 7412 ) / 17
LCM(731,7412) = 5418172 / 17
LCM(731,7412) = 318716
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FAQs on GCF of Fractions of 8082/731, 9829/7412
1. What is the HCF of 8082,9829?
The HCF of 8082,9829 is 1
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 8082/731, 9829/7412?
Answer: GCF of Numerators as per given numbers 8082/731, 9829/7412 is
GCF of Numerators i.e. for 8082,9829 is 1
LCM of denominators i.e. for 731,7412 is 318716.
Thus, GCF of Fractions is 1/318716.Finally, GCF of Fractions for 8082/731, 9829/7412 is 1/318716.