GCF of 3009/830, 7311/1666
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3009/830, 7311/1666 i.e 3/691390 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3009/830, 7311/1666.
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 3009/830,7311/1666?
Given fractions are 3009/830,7311/1666
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 3009/830,7311/1666, numerators are 3009,7311
Denominators are 830,1666
The GCF of 3009,7311 is 3 .
LCM of 830,1666 is 691390.
The greatest common factor of 3009/830,7311/1666 = [GCF of 3009,7311]/[LCM of 830,1666]= 3/691390
Therefore, the GCF of 3009/830,7311/1666 is 3/691390.
To find the highest common factor of 3009,7311, we have to find the factors of both numbers and list the highest common factor.
The factors of 3009 are 1, 3, 17, 51, 59, 177, 1003, 3009
The factors of 7311 are 1, 3, 2437, 7311
The HCF of 3009,7311 is 3.
Lets's calculate GCF of 3009,7311
| 3 | 3009, 7311 |
| 1003, 2437 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 3009,7311 By Matching Biggest Common Factor Method
Now, list down the factors of 3009
:1,3,17,51,59,177,1003,3009
Now, list down the factors of 7311
:1,3,2437,7311
Greatest Common Factor
We found the factors 3009,7311 . The biggest common factor number is the GCF number.
So the greatest common factor 3009,7311 is 3.
Lets's calculate LCM of 830,1666
| 2 | 830, 1666 |
| 415, 833 |
∴ So the LCM of the given numbers is 2 x 415 x 833 = 691390
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/691390
Therefore, the GCF of Fractions 3009/830,7311/1666 is 3/691390
Least Common Multiple of 830,1666 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 830,1666 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(830,1666) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(830,1666) x common factors =2 x 1 = 2
LCM(830,1666) = ( 830 × 1666 ) / 2
LCM(830,1666) = 1382780 / 2
LCM(830,1666) = 691390
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FAQs on GCF of Fractions of 3009/830, 7311/1666
1. What is the HCF of 3009,7311?
The HCF of 3009,7311 is 3
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 3009/830, 7311/1666?
Answer: GCF of Numerators as per given numbers 3009/830, 7311/1666 is
GCF of Numerators i.e. for 3009,7311 is 3
LCM of denominators i.e. for 830,1666 is 691390.
Thus, GCF of Fractions is 3/691390.Finally, GCF of Fractions for 3009/830, 7311/1666 is 3/691390.