GCF of 3780/820, 4074/7869
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3780/820, 4074/7869 i.e 42/6452580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3780/820, 4074/7869.
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 3780/820,4074/7869?
Given fractions are 3780/820,4074/7869
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 3780/820,4074/7869, numerators are 3780,4074
Denominators are 820,7869
The GCF of 3780,4074 is 42 .
LCM of 820,7869 is 6452580.
The greatest common factor of 3780/820,4074/7869 = [GCF of 3780,4074]/[LCM of 820,7869]= 42/6452580
Therefore, the GCF of 3780/820,4074/7869 is 42/6452580.
To find the highest common factor of 3780,4074, we have to find the factors of both numbers and list the highest common factor.
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 factors of 4074 are 1, 2, 3, 6, 7, 14, 21, 42, 97, 194, 291, 582, 679, 1358, 2037, 4074
The HCF of 3780,4074 is 42.
Lets's calculate GCF of 3780,4074
| 2 | 3780, 4074 |
| 3 | 1890, 2037 |
| 7 | 630, 679 |
| 90, 97 |
∴ So the GCF of the given numbers is 2 x 3 x 7 = 42
Greatest Common Factor of 3780,4074 By Matching Biggest Common Factor Method
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
Now, list down the factors of 4074
:1,2,3,6,7,14,21,42,97,194,291,582,679,1358,2037,4074
Greatest Common Factor
We found the factors 3780,4074 . The biggest common factor number is the GCF number.
So the greatest common factor 3780,4074 is 42.
Lets's calculate LCM of 820,7869
Given numbers has no common factors except 1. So, there LCM is their product i.e 6452580
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 42/6452580
Therefore, the GCF of Fractions 3780/820,4074/7869 is 42/6452580
Least Common Multiple of 820,7869 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 820,7869 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(820,7869) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(820,7869) x common factors =1 x 1 = 1
LCM(820,7869) = ( 820 × 7869 ) / 1
LCM(820,7869) = 6452580 / 1
LCM(820,7869) = 6452580
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 3780/820, 4074/7869
1. What is the HCF of 3780,4074?
The HCF of 3780,4074 is 42
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 3780/820, 4074/7869?
Answer: GCF of Numerators as per given numbers 3780/820, 4074/7869 is
GCF of Numerators i.e. for 3780,4074 is 42
LCM of denominators i.e. for 820,7869 is 6452580.
Thus, GCF of Fractions is 42/6452580.Finally, GCF of Fractions for 3780/820, 4074/7869 is 42/6452580.