GCF of 7005/834, 1638/582
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7005/834, 1638/582 i.e 3/80898 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7005/834, 1638/582.
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 7005/834,1638/582?
Given fractions are 7005/834,1638/582
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 7005/834,1638/582, numerators are 7005,1638
Denominators are 834,582
The GCF of 7005,1638 is 3 .
LCM of 834,582 is 80898.
The greatest common factor of 7005/834,1638/582 = [GCF of 7005,1638]/[LCM of 834,582]= 3/80898
Therefore, the GCF of 7005/834,1638/582 is 3/80898.
To find the highest common factor of 7005,1638, we have to find the factors of both numbers and list the highest common factor.
The factors of 7005 are 1, 3, 5, 15, 467, 1401, 2335, 7005
The factors of 1638 are 1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 39, 42, 63, 78, 91, 117, 126, 182, 234, 273, 546, 819, 1638
The HCF of 7005,1638 is 3.
Lets's calculate GCF of 7005,1638
| 3 | 7005, 1638 |
| 2335, 546 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7005,1638 By Matching Biggest Common Factor Method
Now, list down the factors of 7005
:1,3,5,15,467,1401,2335,7005
Now, list down the factors of 1638
:1,2,3,6,7,9,13,14,18,21,26,39,42,63,78,91,117,126,182,234,273,546,819,1638
Greatest Common Factor
We found the factors 7005,1638 . The biggest common factor number is the GCF number.
So the greatest common factor 7005,1638 is 3.
Lets's calculate LCM of 834,582
| 2 | 834, 582 |
| 3 | 417, 291 |
| 139, 97 |
∴ So the LCM of the given numbers is 2 x 3 x 139 x 97 = 80898
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/80898
Therefore, the GCF of Fractions 7005/834,1638/582 is 3/80898
Least Common Multiple of 834,582 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 834,582 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(834,582) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(834,582) x common factors =6 x 1 = 6
LCM(834,582) = ( 834 × 582 ) / 6
LCM(834,582) = 485388 / 6
LCM(834,582) = 80898
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FAQs on GCF of Fractions of 7005/834, 1638/582
1. What is the HCF of 7005,1638?
The HCF of 7005,1638 is 3
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 7005/834, 1638/582?
Answer: GCF of Numerators as per given numbers 7005/834, 1638/582 is
GCF of Numerators i.e. for 7005,1638 is 3
LCM of denominators i.e. for 834,582 is 80898.
Thus, GCF of Fractions is 3/80898.Finally, GCF of Fractions for 7005/834, 1638/582 is 3/80898.