GCF of 1809/684, 3742/4560
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1809/684, 3742/4560 i.e 1/13680 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1809/684, 3742/4560.
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 1809/684,3742/4560?
Given fractions are 1809/684,3742/4560
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 1809/684,3742/4560, numerators are 1809,3742
Denominators are 684,4560
The GCF of 1809,3742 is 1 .
LCM of 684,4560 is 13680.
The greatest common factor of 1809/684,3742/4560 = [GCF of 1809,3742]/[LCM of 684,4560]= 1/13680
Therefore, the GCF of 1809/684,3742/4560 is 1/13680.
To find the highest common factor of 1809,3742, we have to find the factors of both numbers and list the highest common factor.
The factors of 1809 are 1, 3, 9, 27, 67, 201, 603, 1809
The factors of 3742 are 1, 2, 1871, 3742
The HCF of 1809,3742 is 1.
Lets's calculate GCF of 1809,3742
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1809,3742 By Matching Biggest Common Factor Method
Now, list down the factors of 1809
:1,3,9,27,67,201,603,1809
Now, list down the factors of 3742
:1,2,1871,3742
Greatest Common Factor
We found the factors 1809,3742 . The biggest common factor number is the GCF number.
So the greatest common factor 1809,3742 is 1.
Lets's calculate LCM of 684,4560
| 2 | 684, 4560 |
| 2 | 342, 2280 |
| 3 | 171, 1140 |
| 19 | 57, 380 |
| 3, 20 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 19 x 3 x 20 = 13680
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13680
Therefore, the GCF of Fractions 1809/684,3742/4560 is 1/13680
Least Common Multiple of 684,4560 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 684,4560 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(684,4560) = 228
common factors(in case of two or more numbers have common factors) = 1
GCF(684,4560) x common factors =228 x 1 = 228
LCM(684,4560) = ( 684 × 4560 ) / 228
LCM(684,4560) = 3119040 / 228
LCM(684,4560) = 13680
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FAQs on GCF of Fractions of 1809/684, 3742/4560
1. What is the HCF of 1809,3742?
The HCF of 1809,3742 is 1
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 1809/684, 3742/4560?
Answer: GCF of Numerators as per given numbers 1809/684, 3742/4560 is
GCF of Numerators i.e. for 1809,3742 is 1
LCM of denominators i.e. for 684,4560 is 13680.
Thus, GCF of Fractions is 1/13680.Finally, GCF of Fractions for 1809/684, 3742/4560 is 1/13680.