GCF of 3415/390, 5740/5506
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3415/390, 5740/5506 i.e 5/1073670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3415/390, 5740/5506.
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 3415/390,5740/5506?
Given fractions are 3415/390,5740/5506
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 3415/390,5740/5506, numerators are 3415,5740
Denominators are 390,5506
The GCF of 3415,5740 is 5 .
LCM of 390,5506 is 1073670.
The greatest common factor of 3415/390,5740/5506 = [GCF of 3415,5740]/[LCM of 390,5506]= 5/1073670
Therefore, the GCF of 3415/390,5740/5506 is 5/1073670.
To find the highest common factor of 3415,5740, we have to find the factors of both numbers and list the highest common factor.
The factors of 3415 are 1, 5, 683, 3415
The factors of 5740 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 41, 70, 82, 140, 164, 205, 287, 410, 574, 820, 1148, 1435, 2870, 5740
The HCF of 3415,5740 is 5.
Lets's calculate GCF of 3415,5740
| 5 | 3415, 5740 |
| 683, 1148 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 3415,5740 By Matching Biggest Common Factor Method
Now, list down the factors of 3415
:1,5,683,3415
Now, list down the factors of 5740
:1,2,4,5,7,10,14,20,28,35,41,70,82,140,164,205,287,410,574,820,1148,1435,2870,5740
Greatest Common Factor
We found the factors 3415,5740 . The biggest common factor number is the GCF number.
So the greatest common factor 3415,5740 is 5.
Lets's calculate LCM of 390,5506
| 2 | 390, 5506 |
| 195, 2753 |
∴ So the LCM of the given numbers is 2 x 195 x 2753 = 1073670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/1073670
Therefore, the GCF of Fractions 3415/390,5740/5506 is 5/1073670
Least Common Multiple of 390,5506 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 390,5506 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(390,5506) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(390,5506) x common factors =2 x 1 = 2
LCM(390,5506) = ( 390 × 5506 ) / 2
LCM(390,5506) = 2147340 / 2
LCM(390,5506) = 1073670
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FAQs on GCF of Fractions of 3415/390, 5740/5506
1. What is the HCF of 3415,5740?
The HCF of 3415,5740 is 5
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 3415/390, 5740/5506?
Answer: GCF of Numerators as per given numbers 3415/390, 5740/5506 is
GCF of Numerators i.e. for 3415,5740 is 5
LCM of denominators i.e. for 390,5506 is 1073670.
Thus, GCF of Fractions is 5/1073670.Finally, GCF of Fractions for 3415/390, 5740/5506 is 5/1073670.