GCF of 5838/281, 1584/617
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5838/281, 1584/617 i.e 6/173377 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5838/281, 1584/617.
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 5838/281,1584/617?
Given fractions are 5838/281,1584/617
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 5838/281,1584/617, numerators are 5838,1584
Denominators are 281,617
The GCF of 5838,1584 is 6 .
LCM of 281,617 is 173377.
The greatest common factor of 5838/281,1584/617 = [GCF of 5838,1584]/[LCM of 281,617]= 6/173377
Therefore, the GCF of 5838/281,1584/617 is 6/173377.
To find the highest common factor of 5838,1584, we have to find the factors of both numbers and list the highest common factor.
The factors of 5838 are 1, 2, 3, 6, 7, 14, 21, 42, 139, 278, 417, 834, 973, 1946, 2919, 5838
The factors of 1584 are 1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 33, 36, 44, 48, 66, 72, 88, 99, 132, 144, 176, 198, 264, 396, 528, 792, 1584
The HCF of 5838,1584 is 6.
Lets's calculate GCF of 5838,1584
| 2 | 5838, 1584 |
| 3 | 2919, 792 |
| 973, 264 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 5838,1584 By Matching Biggest Common Factor Method
Now, list down the factors of 5838
:1,2,3,6,7,14,21,42,139,278,417,834,973,1946,2919,5838
Now, list down the factors of 1584
:1,2,3,4,6,8,9,11,12,16,18,22,24,33,36,44,48,66,72,88,99,132,144,176,198,264,396,528,792,1584
Greatest Common Factor
We found the factors 5838,1584 . The biggest common factor number is the GCF number.
So the greatest common factor 5838,1584 is 6.
Lets's calculate LCM of 281,617
Given numbers has no common factors except 1. So, there LCM is their product i.e 173377
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/173377
Therefore, the GCF of Fractions 5838/281,1584/617 is 6/173377
Least Common Multiple of 281,617 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 281,617 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(281,617) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(281,617) x common factors =1 x 1 = 1
LCM(281,617) = ( 281 × 617 ) / 1
LCM(281,617) = 173377 / 1
LCM(281,617) = 173377
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FAQs on GCF of Fractions of 5838/281, 1584/617
1. What is the HCF of 5838,1584?
The HCF of 5838,1584 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 5838/281, 1584/617?
Answer: GCF of Numerators as per given numbers 5838/281, 1584/617 is
GCF of Numerators i.e. for 5838,1584 is 6
LCM of denominators i.e. for 281,617 is 173377.
Thus, GCF of Fractions is 6/173377.Finally, GCF of Fractions for 5838/281, 1584/617 is 6/173377.