GCF of 1578/806, 1188/268
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1578/806, 1188/268 i.e 6/108004 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1578/806, 1188/268.
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 1578/806,1188/268?
Given fractions are 1578/806,1188/268
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 1578/806,1188/268, numerators are 1578,1188
Denominators are 806,268
The GCF of 1578,1188 is 6 .
LCM of 806,268 is 108004.
The greatest common factor of 1578/806,1188/268 = [GCF of 1578,1188]/[LCM of 806,268]= 6/108004
Therefore, the GCF of 1578/806,1188/268 is 6/108004.
To find the highest common factor of 1578,1188, we have to find the factors of both numbers and list the highest common factor.
The factors of 1578 are 1, 2, 3, 6, 263, 526, 789, 1578
The factors of 1188 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 27, 33, 36, 44, 54, 66, 99, 108, 132, 198, 297, 396, 594, 1188
The HCF of 1578,1188 is 6.
Lets's calculate GCF of 1578,1188
| 2 | 1578, 1188 |
| 3 | 789, 594 |
| 263, 198 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 1578,1188 By Matching Biggest Common Factor Method
Now, list down the factors of 1578
:1,2,3,6,263,526,789,1578
Now, list down the factors of 1188
:1,2,3,4,6,9,11,12,18,22,27,33,36,44,54,66,99,108,132,198,297,396,594,1188
Greatest Common Factor
We found the factors 1578,1188 . The biggest common factor number is the GCF number.
So the greatest common factor 1578,1188 is 6.
Lets's calculate LCM of 806,268
| 2 | 806, 268 |
| 403, 134 |
∴ So the LCM of the given numbers is 2 x 403 x 134 = 108004
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/108004
Therefore, the GCF of Fractions 1578/806,1188/268 is 6/108004
Least Common Multiple of 806,268 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 806,268 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(806,268) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(806,268) x common factors =2 x 1 = 2
LCM(806,268) = ( 806 × 268 ) / 2
LCM(806,268) = 216008 / 2
LCM(806,268) = 108004
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FAQs on GCF of Fractions of 1578/806, 1188/268
1. What is the HCF of 1578,1188?
The HCF of 1578,1188 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 1578/806, 1188/268?
Answer: GCF of Numerators as per given numbers 1578/806, 1188/268 is
GCF of Numerators i.e. for 1578,1188 is 6
LCM of denominators i.e. for 806,268 is 108004.
Thus, GCF of Fractions is 6/108004.Finally, GCF of Fractions for 1578/806, 1188/268 is 6/108004.