GCF of 8238/685, 7140/6871
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8238/685, 7140/6871 i.e 6/4706635 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8238/685, 7140/6871.
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 8238/685,7140/6871?
Given fractions are 8238/685,7140/6871
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 8238/685,7140/6871, numerators are 8238,7140
Denominators are 685,6871
The GCF of 8238,7140 is 6 .
LCM of 685,6871 is 4706635.
The greatest common factor of 8238/685,7140/6871 = [GCF of 8238,7140]/[LCM of 685,6871]= 6/4706635
Therefore, the GCF of 8238/685,7140/6871 is 6/4706635.
To find the highest common factor of 8238,7140, we have to find the factors of both numbers and list the highest common factor.
The factors of 8238 are 1, 2, 3, 6, 1373, 2746, 4119, 8238
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 8238,7140 is 6.
Lets's calculate GCF of 8238,7140
| 2 | 8238, 7140 |
| 3 | 4119, 3570 |
| 1373, 1190 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 8238,7140 By Matching Biggest Common Factor Method
Now, list down the factors of 8238
:1,2,3,6,1373,2746,4119,8238
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 8238,7140 . The biggest common factor number is the GCF number.
So the greatest common factor 8238,7140 is 6.
Lets's calculate LCM of 685,6871
Given numbers has no common factors except 1. So, there LCM is their product i.e 4706635
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/4706635
Therefore, the GCF of Fractions 8238/685,7140/6871 is 6/4706635
Least Common Multiple of 685,6871 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 685,6871 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(685,6871) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(685,6871) x common factors =1 x 1 = 1
LCM(685,6871) = ( 685 × 6871 ) / 1
LCM(685,6871) = 4706635 / 1
LCM(685,6871) = 4706635
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FAQs on GCF of Fractions of 8238/685, 7140/6871
1. What is the HCF of 8238,7140?
The HCF of 8238,7140 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 8238/685, 7140/6871?
Answer: GCF of Numerators as per given numbers 8238/685, 7140/6871 is
GCF of Numerators i.e. for 8238,7140 is 6
LCM of denominators i.e. for 685,6871 is 4706635.
Thus, GCF of Fractions is 6/4706635.Finally, GCF of Fractions for 8238/685, 7140/6871 is 6/4706635.