GCF of 5782/982, 7280/8146
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5782/982, 7280/8146 i.e 14/3999686 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5782/982, 7280/8146.
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 5782/982,7280/8146?
Given fractions are 5782/982,7280/8146
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 5782/982,7280/8146, numerators are 5782,7280
Denominators are 982,8146
The GCF of 5782,7280 is 14 .
LCM of 982,8146 is 3999686.
The greatest common factor of 5782/982,7280/8146 = [GCF of 5782,7280]/[LCM of 982,8146]= 14/3999686
Therefore, the GCF of 5782/982,7280/8146 is 14/3999686.
To find the highest common factor of 5782,7280, we have to find the factors of both numbers and list the highest common factor.
The factors of 5782 are 1, 2, 7, 14, 49, 59, 98, 118, 413, 826, 2891, 5782
The factors of 7280 are 1, 2, 4, 5, 7, 8, 10, 13, 14, 16, 20, 26, 28, 35, 40, 52, 56, 65, 70, 80, 91, 104, 112, 130, 140, 182, 208, 260, 280, 364, 455, 520, 560, 728, 910, 1040, 1456, 1820, 3640, 7280
The HCF of 5782,7280 is 14.
Lets's calculate GCF of 5782,7280
| 2 | 5782, 7280 |
| 7 | 2891, 3640 |
| 413, 520 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 5782,7280 By Matching Biggest Common Factor Method
Now, list down the factors of 5782
:1,2,7,14,49,59,98,118,413,826,2891,5782
Now, list down the factors of 7280
:1,2,4,5,7,8,10,13,14,16,20,26,28,35,40,52,56,65,70,80,91,104,112,130,140,182,208,260,280,364,455,520,560,728,910,1040,1456,1820,3640,7280
Greatest Common Factor
We found the factors 5782,7280 . The biggest common factor number is the GCF number.
So the greatest common factor 5782,7280 is 14.
Lets's calculate LCM of 982,8146
| 2 | 982, 8146 |
| 491, 4073 |
∴ So the LCM of the given numbers is 2 x 491 x 4073 = 3999686
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/3999686
Therefore, the GCF of Fractions 5782/982,7280/8146 is 14/3999686
Least Common Multiple of 982,8146 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 982,8146 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(982,8146) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(982,8146) x common factors =2 x 1 = 2
LCM(982,8146) = ( 982 × 8146 ) / 2
LCM(982,8146) = 7999372 / 2
LCM(982,8146) = 3999686
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 5782/982, 7280/8146
1. What is the HCF of 5782,7280?
The HCF of 5782,7280 is 14
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 5782/982, 7280/8146?
Answer: GCF of Numerators as per given numbers 5782/982, 7280/8146 is
GCF of Numerators i.e. for 5782,7280 is 14
LCM of denominators i.e. for 982,8146 is 3999686.
Thus, GCF of Fractions is 14/3999686.Finally, GCF of Fractions for 5782/982, 7280/8146 is 14/3999686.