GCF of 6682/546, 7140/2779
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6682/546, 7140/2779 i.e 2/216762 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6682/546, 7140/2779.
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 6682/546,7140/2779?
Given fractions are 6682/546,7140/2779
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 6682/546,7140/2779, numerators are 6682,7140
Denominators are 546,2779
The GCF of 6682,7140 is 2 .
LCM of 546,2779 is 216762.
The greatest common factor of 6682/546,7140/2779 = [GCF of 6682,7140]/[LCM of 546,2779]= 2/216762
Therefore, the GCF of 6682/546,7140/2779 is 2/216762.
To find the highest common factor of 6682,7140, we have to find the factors of both numbers and list the highest common factor.
The factors of 6682 are 1, 2, 13, 26, 257, 514, 3341, 6682
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 HCF of 6682,7140 is 2.
Lets's calculate GCF of 6682,7140
| 2 | 6682, 7140 |
| 3341, 3570 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 6682,7140 By Matching Biggest Common Factor Method
Now, list down the factors of 6682
:1,2,13,26,257,514,3341,6682
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
Greatest Common Factor
We found the factors 6682,7140 . The biggest common factor number is the GCF number.
So the greatest common factor 6682,7140 is 2.
Lets's calculate LCM of 546,2779
| 7 | 546, 2779 |
| 78, 397 |
∴ So the LCM of the given numbers is 7 x 78 x 397 = 216762
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/216762
Therefore, the GCF of Fractions 6682/546,7140/2779 is 2/216762
Least Common Multiple of 546,2779 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 546,2779 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(546,2779) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(546,2779) x common factors =7 x 1 = 7
LCM(546,2779) = ( 546 × 2779 ) / 7
LCM(546,2779) = 1517334 / 7
LCM(546,2779) = 216762
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FAQs on GCF of Fractions of 6682/546, 7140/2779
1. What is the HCF of 6682,7140?
The HCF of 6682,7140 is 2
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 6682/546, 7140/2779?
Answer: GCF of Numerators as per given numbers 6682/546, 7140/2779 is
GCF of Numerators i.e. for 6682,7140 is 2
LCM of denominators i.e. for 546,2779 is 216762.
Thus, GCF of Fractions is 2/216762.Finally, GCF of Fractions for 6682/546, 7140/2779 is 2/216762.