GCF of 7140/729, 3978/510
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7140/729, 3978/510 i.e 102/123930 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7140/729, 3978/510.
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 7140/729,3978/510?
Given fractions are 7140/729,3978/510
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 7140/729,3978/510, numerators are 7140,3978
Denominators are 729,510
The GCF of 7140,3978 is 102 .
LCM of 729,510 is 123930.
The greatest common factor of 7140/729,3978/510 = [GCF of 7140,3978]/[LCM of 729,510]= 102/123930
Therefore, the GCF of 7140/729,3978/510 is 102/123930.
To find the highest common factor of 7140,3978, we have to find the factors of both numbers and list the highest common factor.
The factors of 7140 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 17, 20, 21, 28, 30, 34, 35, 42, 51, 60, 68, 70, 84, 85, 102, 105, 119, 140, 170, 204, 210, 238, 255, 340, 357, 420, 476, 510, 595, 714, 1020, 1190, 1428, 1785, 2380, 3570, 7140
The factors of 3978 are 1, 2, 3, 6, 9, 13, 17, 18, 26, 34, 39, 51, 78, 102, 117, 153, 221, 234, 306, 442, 663, 1326, 1989, 3978
The HCF of 7140,3978 is 102.
Lets's calculate GCF of 7140,3978
| 2 | 7140, 3978 |
| 3 | 3570, 1989 |
| 17 | 1190, 663 |
| 70, 39 |
∴ So the GCF of the given numbers is 2 x 3 x 17 = 102
Greatest Common Factor of 7140,3978 By Matching Biggest Common Factor Method
Now, list down the factors of 7140
:1,2,3,4,5,6,7,10,12,14,15,17,20,21,28,30,34,35,42,51,60,68,70,84,85,102,105,119,140,170,204,210,238,255,340,357,420,476,510,595,714,1020,1190,1428,1785,2380,3570,7140
Now, list down the factors of 3978
:1,2,3,6,9,13,17,18,26,34,39,51,78,102,117,153,221,234,306,442,663,1326,1989,3978
Greatest Common Factor
We found the factors 7140,3978 . The biggest common factor number is the GCF number.
So the greatest common factor 7140,3978 is 102.
Lets's calculate LCM of 729,510
| 3 | 729, 510 |
| 243, 170 |
∴ So the LCM of the given numbers is 3 x 243 x 170 = 123930
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 102/123930
Therefore, the GCF of Fractions 7140/729,3978/510 is 102/123930
Least Common Multiple of 729,510 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 729,510 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(729,510) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(729,510) x common factors =3 x 1 = 3
LCM(729,510) = ( 729 × 510 ) / 3
LCM(729,510) = 371790 / 3
LCM(729,510) = 123930
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FAQs on GCF of Fractions of 7140/729, 3978/510
1. What is the HCF of 7140,3978?
The HCF of 7140,3978 is 102
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 7140/729, 3978/510?
Answer: GCF of Numerators as per given numbers 7140/729, 3978/510 is
GCF of Numerators i.e. for 7140,3978 is 102
LCM of denominators i.e. for 729,510 is 123930.
Thus, GCF of Fractions is 102/123930.Finally, GCF of Fractions for 7140/729, 3978/510 is 102/123930.