GCF of 1649/83, 3060/586
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1649/83, 3060/586 i.e 17/48638 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1649/83, 3060/586.
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 1649/83,3060/586?
Given fractions are 1649/83,3060/586
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 1649/83,3060/586, numerators are 1649,3060
Denominators are 83,586
The GCF of 1649,3060 is 17 .
LCM of 83,586 is 48638.
The greatest common factor of 1649/83,3060/586 = [GCF of 1649,3060]/[LCM of 83,586]= 17/48638
Therefore, the GCF of 1649/83,3060/586 is 17/48638.
To find the highest common factor of 1649,3060, we have to find the factors of both numbers and list the highest common factor.
The factors of 1649 are 1, 17, 97, 1649
The factors of 3060 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 17, 18, 20, 30, 34, 36, 45, 51, 60, 68, 85, 90, 102, 153, 170, 180, 204, 255, 306, 340, 510, 612, 765, 1020, 1530, 3060
The HCF of 1649,3060 is 17.
Lets's calculate GCF of 1649,3060
| 17 | 1649, 3060 |
| 97, 180 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 1649,3060 By Matching Biggest Common Factor Method
Now, list down the factors of 1649
:1,17,97,1649
Now, list down the factors of 3060
:1,2,3,4,5,6,9,10,12,15,17,18,20,30,34,36,45,51,60,68,85,90,102,153,170,180,204,255,306,340,510,612,765,1020,1530,3060
Greatest Common Factor
We found the factors 1649,3060 . The biggest common factor number is the GCF number.
So the greatest common factor 1649,3060 is 17.
Lets's calculate LCM of 83,586
Given numbers has no common factors except 1. So, there LCM is their product i.e 48638
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/48638
Therefore, the GCF of Fractions 1649/83,3060/586 is 17/48638
Least Common Multiple of 83,586 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 83,586 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(83,586) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(83,586) x common factors =1 x 1 = 1
LCM(83,586) = ( 83 × 586 ) / 1
LCM(83,586) = 48638 / 1
LCM(83,586) = 48638
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FAQs on GCF of Fractions of 1649/83, 3060/586
1. What is the HCF of 1649,3060?
The HCF of 1649,3060 is 17
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 1649/83, 3060/586?
Answer: GCF of Numerators as per given numbers 1649/83, 3060/586 is
GCF of Numerators i.e. for 1649,3060 is 17
LCM of denominators i.e. for 83,586 is 48638.
Thus, GCF of Fractions is 17/48638.Finally, GCF of Fractions for 1649/83, 3060/586 is 17/48638.