GCF of 3663/509, 1980/671
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3663/509, 1980/671 i.e 99/341539 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3663/509, 1980/671.
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 3663/509,1980/671?
Given fractions are 3663/509,1980/671
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 3663/509,1980/671, numerators are 3663,1980
Denominators are 509,671
The GCF of 3663,1980 is 99 .
LCM of 509,671 is 341539.
The greatest common factor of 3663/509,1980/671 = [GCF of 3663,1980]/[LCM of 509,671]= 99/341539
Therefore, the GCF of 3663/509,1980/671 is 99/341539.
To find the highest common factor of 3663,1980, we have to find the factors of both numbers and list the highest common factor.
The factors of 3663 are 1, 3, 9, 11, 33, 37, 99, 111, 333, 407, 1221, 3663
The factors of 1980 are 1, 2, 3, 4, 5, 6, 9, 10, 11, 12, 15, 18, 20, 22, 30, 33, 36, 44, 45, 55, 60, 66, 90, 99, 110, 132, 165, 180, 198, 220, 330, 396, 495, 660, 990, 1980
The HCF of 3663,1980 is 99.
Lets's calculate GCF of 3663,1980
| 3 | 3663, 1980 |
| 3 | 1221, 660 |
| 11 | 407, 220 |
| 37, 20 |
∴ So the GCF of the given numbers is 3 x 3 x 11 = 99
Greatest Common Factor of 3663,1980 By Matching Biggest Common Factor Method
Now, list down the factors of 3663
:1,3,9,11,33,37,99,111,333,407,1221,3663
Now, list down the factors of 1980
:1,2,3,4,5,6,9,10,11,12,15,18,20,22,30,33,36,44,45,55,60,66,90,99,110,132,165,180,198,220,330,396,495,660,990,1980
Greatest Common Factor
We found the factors 3663,1980 . The biggest common factor number is the GCF number.
So the greatest common factor 3663,1980 is 99.
Lets's calculate LCM of 509,671
Given numbers has no common factors except 1. So, there LCM is their product i.e 341539
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 99/341539
Therefore, the GCF of Fractions 3663/509,1980/671 is 99/341539
Least Common Multiple of 509,671 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 509,671 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(509,671) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(509,671) x common factors =1 x 1 = 1
LCM(509,671) = ( 509 × 671 ) / 1
LCM(509,671) = 341539 / 1
LCM(509,671) = 341539
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FAQs on GCF of Fractions of 3663/509, 1980/671
1. What is the HCF of 3663,1980?
The HCF of 3663,1980 is 99
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 3663/509, 1980/671?
Answer: GCF of Numerators as per given numbers 3663/509, 1980/671 is
GCF of Numerators i.e. for 3663,1980 is 99
LCM of denominators i.e. for 509,671 is 341539.
Thus, GCF of Fractions is 99/341539.Finally, GCF of Fractions for 3663/509, 1980/671 is 99/341539.