GCF of 8502/270, 2982/6164
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8502/270, 2982/6164 i.e 6/832140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8502/270, 2982/6164.
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 8502/270,2982/6164?
Given fractions are 8502/270,2982/6164
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 8502/270,2982/6164, numerators are 8502,2982
Denominators are 270,6164
The GCF of 8502,2982 is 6 .
LCM of 270,6164 is 832140.
The greatest common factor of 8502/270,2982/6164 = [GCF of 8502,2982]/[LCM of 270,6164]= 6/832140
Therefore, the GCF of 8502/270,2982/6164 is 6/832140.
To find the highest common factor of 8502,2982, we have to find the factors of both numbers and list the highest common factor.
The factors of 8502 are 1, 2, 3, 6, 13, 26, 39, 78, 109, 218, 327, 654, 1417, 2834, 4251, 8502
The factors of 2982 are 1, 2, 3, 6, 7, 14, 21, 42, 71, 142, 213, 426, 497, 994, 1491, 2982
The HCF of 8502,2982 is 6.
Lets's calculate GCF of 8502,2982
| 2 | 8502, 2982 |
| 3 | 4251, 1491 |
| 1417, 497 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 8502,2982 By Matching Biggest Common Factor Method
Now, list down the factors of 8502
:1,2,3,6,13,26,39,78,109,218,327,654,1417,2834,4251,8502
Now, list down the factors of 2982
:1,2,3,6,7,14,21,42,71,142,213,426,497,994,1491,2982
Greatest Common Factor
We found the factors 8502,2982 . The biggest common factor number is the GCF number.
So the greatest common factor 8502,2982 is 6.
Lets's calculate LCM of 270,6164
| 2 | 270, 6164 |
| 135, 3082 |
∴ So the LCM of the given numbers is 2 x 135 x 3082 = 832140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/832140
Therefore, the GCF of Fractions 8502/270,2982/6164 is 6/832140
Least Common Multiple of 270,6164 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 270,6164 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(270,6164) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(270,6164) x common factors =2 x 1 = 2
LCM(270,6164) = ( 270 × 6164 ) / 2
LCM(270,6164) = 1664280 / 2
LCM(270,6164) = 832140
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FAQs on GCF of Fractions of 8502/270, 2982/6164
1. What is the HCF of 8502,2982?
The HCF of 8502,2982 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 8502/270, 2982/6164?
Answer: GCF of Numerators as per given numbers 8502/270, 2982/6164 is
GCF of Numerators i.e. for 8502,2982 is 6
LCM of denominators i.e. for 270,6164 is 832140.
Thus, GCF of Fractions is 6/832140.Finally, GCF of Fractions for 8502/270, 2982/6164 is 6/832140.