GCF of 1728/876, 7038/6339
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1728/876, 7038/6339 i.e 18/1850988 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1728/876, 7038/6339.
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 1728/876,7038/6339?
Given fractions are 1728/876,7038/6339
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 1728/876,7038/6339, numerators are 1728,7038
Denominators are 876,6339
The GCF of 1728,7038 is 18 .
LCM of 876,6339 is 1850988.
The greatest common factor of 1728/876,7038/6339 = [GCF of 1728,7038]/[LCM of 876,6339]= 18/1850988
Therefore, the GCF of 1728/876,7038/6339 is 18/1850988.
To find the highest common factor of 1728,7038, we have to find the factors of both numbers and list the highest common factor.
The factors of 1728 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 96, 108, 144, 192, 216, 288, 432, 576, 864, 1728
The factors of 7038 are 1, 2, 3, 6, 9, 17, 18, 23, 34, 46, 51, 69, 102, 138, 153, 207, 306, 391, 414, 782, 1173, 2346, 3519, 7038
The HCF of 1728,7038 is 18.
Lets's calculate GCF of 1728,7038
| 2 | 1728, 7038 |
| 3 | 864, 3519 |
| 3 | 288, 1173 |
| 96, 391 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 1728,7038 By Matching Biggest Common Factor Method
Now, list down the factors of 1728
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,96,108,144,192,216,288,432,576,864,1728
Now, list down the factors of 7038
:1,2,3,6,9,17,18,23,34,46,51,69,102,138,153,207,306,391,414,782,1173,2346,3519,7038
Greatest Common Factor
We found the factors 1728,7038 . The biggest common factor number is the GCF number.
So the greatest common factor 1728,7038 is 18.
Lets's calculate LCM of 876,6339
| 3 | 876, 6339 |
| 292, 2113 |
∴ So the LCM of the given numbers is 3 x 292 x 2113 = 1850988
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/1850988
Therefore, the GCF of Fractions 1728/876,7038/6339 is 18/1850988
Least Common Multiple of 876,6339 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 876,6339 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(876,6339) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(876,6339) x common factors =3 x 1 = 3
LCM(876,6339) = ( 876 × 6339 ) / 3
LCM(876,6339) = 5552964 / 3
LCM(876,6339) = 1850988
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FAQs on GCF of Fractions of 1728/876, 7038/6339
1. What is the HCF of 1728,7038?
The HCF of 1728,7038 is 18
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 1728/876, 7038/6339?
Answer: GCF of Numerators as per given numbers 1728/876, 7038/6339 is
GCF of Numerators i.e. for 1728,7038 is 18
LCM of denominators i.e. for 876,6339 is 1850988.
Thus, GCF of Fractions is 18/1850988.Finally, GCF of Fractions for 1728/876, 7038/6339 is 18/1850988.