GCF of 1617/490, 8140/866
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1617/490, 8140/866 i.e 11/212170 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1617/490, 8140/866.
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 1617/490,8140/866?
Given fractions are 1617/490,8140/866
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 1617/490,8140/866, numerators are 1617,8140
Denominators are 490,866
The GCF of 1617,8140 is 11 .
LCM of 490,866 is 212170.
The greatest common factor of 1617/490,8140/866 = [GCF of 1617,8140]/[LCM of 490,866]= 11/212170
Therefore, the GCF of 1617/490,8140/866 is 11/212170.
To find the highest common factor of 1617,8140, we have to find the factors of both numbers and list the highest common factor.
The factors of 1617 are 1, 3, 7, 11, 21, 33, 49, 77, 147, 231, 539, 1617
The factors of 8140 are 1, 2, 4, 5, 10, 11, 20, 22, 37, 44, 55, 74, 110, 148, 185, 220, 370, 407, 740, 814, 1628, 2035, 4070, 8140
The HCF of 1617,8140 is 11.
Lets's calculate GCF of 1617,8140
| 11 | 1617, 8140 |
| 147, 740 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 1617,8140 By Matching Biggest Common Factor Method
Now, list down the factors of 1617
:1,3,7,11,21,33,49,77,147,231,539,1617
Now, list down the factors of 8140
:1,2,4,5,10,11,20,22,37,44,55,74,110,148,185,220,370,407,740,814,1628,2035,4070,8140
Greatest Common Factor
We found the factors 1617,8140 . The biggest common factor number is the GCF number.
So the greatest common factor 1617,8140 is 11.
Lets's calculate LCM of 490,866
| 2 | 490, 866 |
| 245, 433 |
∴ So the LCM of the given numbers is 2 x 245 x 433 = 212170
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/212170
Therefore, the GCF of Fractions 1617/490,8140/866 is 11/212170
Least Common Multiple of 490,866 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 490,866 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(490,866) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(490,866) x common factors =2 x 1 = 2
LCM(490,866) = ( 490 × 866 ) / 2
LCM(490,866) = 424340 / 2
LCM(490,866) = 212170
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FAQs on GCF of Fractions of 1617/490, 8140/866
1. What is the HCF of 1617,8140?
The HCF of 1617,8140 is 11
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 1617/490, 8140/866?
Answer: GCF of Numerators as per given numbers 1617/490, 8140/866 is
GCF of Numerators i.e. for 1617,8140 is 11
LCM of denominators i.e. for 490,866 is 212170.
Thus, GCF of Fractions is 11/212170.Finally, GCF of Fractions for 1617/490, 8140/866 is 11/212170.