GCF of 4060/378, 5730/119
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4060/378, 5730/119 i.e 10/6426 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4060/378, 5730/119.
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 4060/378,5730/119?
Given fractions are 4060/378,5730/119
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 4060/378,5730/119, numerators are 4060,5730
Denominators are 378,119
The GCF of 4060,5730 is 10 .
LCM of 378,119 is 6426.
The greatest common factor of 4060/378,5730/119 = [GCF of 4060,5730]/[LCM of 378,119]= 10/6426
Therefore, the GCF of 4060/378,5730/119 is 10/6426.
To find the highest common factor of 4060,5730, we have to find the factors of both numbers and list the highest common factor.
The factors of 4060 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 29, 35, 58, 70, 116, 140, 145, 203, 290, 406, 580, 812, 1015, 2030, 4060
The factors of 5730 are 1, 2, 3, 5, 6, 10, 15, 30, 191, 382, 573, 955, 1146, 1910, 2865, 5730
The HCF of 4060,5730 is 10.
Lets's calculate GCF of 4060,5730
| 2 | 4060, 5730 |
| 5 | 2030, 2865 |
| 406, 573 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 4060,5730 By Matching Biggest Common Factor Method
Now, list down the factors of 4060
:1,2,4,5,7,10,14,20,28,29,35,58,70,116,140,145,203,290,406,580,812,1015,2030,4060
Now, list down the factors of 5730
:1,2,3,5,6,10,15,30,191,382,573,955,1146,1910,2865,5730
Greatest Common Factor
We found the factors 4060,5730 . The biggest common factor number is the GCF number.
So the greatest common factor 4060,5730 is 10.
Lets's calculate LCM of 378,119
| 7 | 378, 119 |
| 54, 17 |
∴ So the LCM of the given numbers is 7 x 54 x 17 = 6426
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/6426
Therefore, the GCF of Fractions 4060/378,5730/119 is 10/6426
Least Common Multiple of 378,119 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 378,119 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,119) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(378,119) x common factors =7 x 1 = 7
LCM(378,119) = ( 378 × 119 ) / 7
LCM(378,119) = 44982 / 7
LCM(378,119) = 6426
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FAQs on GCF of Fractions of 4060/378, 5730/119
1. What is the HCF of 4060,5730?
The HCF of 4060,5730 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 4060/378, 5730/119?
Answer: GCF of Numerators as per given numbers 4060/378, 5730/119 is
GCF of Numerators i.e. for 4060,5730 is 10
LCM of denominators i.e. for 378,119 is 6426.
Thus, GCF of Fractions is 10/6426.Finally, GCF of Fractions for 4060/378, 5730/119 is 10/6426.