GCF of 1810/488, 3780/219
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1810/488, 3780/219 i.e 10/106872 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1810/488, 3780/219.
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 1810/488,3780/219?
Given fractions are 1810/488,3780/219
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 1810/488,3780/219, numerators are 1810,3780
Denominators are 488,219
The GCF of 1810,3780 is 10 .
LCM of 488,219 is 106872.
The greatest common factor of 1810/488,3780/219 = [GCF of 1810,3780]/[LCM of 488,219]= 10/106872
Therefore, the GCF of 1810/488,3780/219 is 10/106872.
To find the highest common factor of 1810,3780, we have to find the factors of both numbers and list the highest common factor.
The factors of 1810 are 1, 2, 5, 10, 181, 362, 905, 1810
The factors of 3780 are 1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 27, 28, 30, 35, 36, 42, 45, 54, 60, 63, 70, 84, 90, 105, 108, 126, 135, 140, 180, 189, 210, 252, 270, 315, 378, 420, 540, 630, 756, 945, 1260, 1890, 3780
The HCF of 1810,3780 is 10.
Lets's calculate GCF of 1810,3780
| 2 | 1810, 3780 |
| 5 | 905, 1890 |
| 181, 378 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 1810,3780 By Matching Biggest Common Factor Method
Now, list down the factors of 1810
:1,2,5,10,181,362,905,1810
Now, list down the factors of 3780
:1,2,3,4,5,6,7,9,10,12,14,15,18,20,21,27,28,30,35,36,42,45,54,60,63,70,84,90,105,108,126,135,140,180,189,210,252,270,315,378,420,540,630,756,945,1260,1890,3780
Greatest Common Factor
We found the factors 1810,3780 . The biggest common factor number is the GCF number.
So the greatest common factor 1810,3780 is 10.
Lets's calculate LCM of 488,219
Given numbers has no common factors except 1. So, there LCM is their product i.e 106872
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/106872
Therefore, the GCF of Fractions 1810/488,3780/219 is 10/106872
Least Common Multiple of 488,219 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 488,219 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(488,219) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(488,219) x common factors =1 x 1 = 1
LCM(488,219) = ( 488 × 219 ) / 1
LCM(488,219) = 106872 / 1
LCM(488,219) = 106872
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FAQs on GCF of Fractions of 1810/488, 3780/219
1. What is the HCF of 1810,3780?
The HCF of 1810,3780 is 10
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 1810/488, 3780/219?
Answer: GCF of Numerators as per given numbers 1810/488, 3780/219 is
GCF of Numerators i.e. for 1810,3780 is 10
LCM of denominators i.e. for 488,219 is 106872.
Thus, GCF of Fractions is 10/106872.Finally, GCF of Fractions for 1810/488, 3780/219 is 10/106872.