GCF of 5355/304, 3915/9584
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5355/304, 3915/9584 i.e 45/182096 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5355/304, 3915/9584.
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 5355/304,3915/9584?
Given fractions are 5355/304,3915/9584
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 5355/304,3915/9584, numerators are 5355,3915
Denominators are 304,9584
The GCF of 5355,3915 is 45 .
LCM of 304,9584 is 182096.
The greatest common factor of 5355/304,3915/9584 = [GCF of 5355,3915]/[LCM of 304,9584]= 45/182096
Therefore, the GCF of 5355/304,3915/9584 is 45/182096.
To find the highest common factor of 5355,3915, we have to find the factors of both numbers and list the highest common factor.
The factors of 5355 are 1, 3, 5, 7, 9, 15, 17, 21, 35, 45, 51, 63, 85, 105, 119, 153, 255, 315, 357, 595, 765, 1071, 1785, 5355
The factors of 3915 are 1, 3, 5, 9, 15, 27, 29, 45, 87, 135, 145, 261, 435, 783, 1305, 3915
The HCF of 5355,3915 is 45.
Lets's calculate GCF of 5355,3915
| 3 | 5355, 3915 |
| 3 | 1785, 1305 |
| 5 | 595, 435 |
| 119, 87 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 5355,3915 By Matching Biggest Common Factor Method
Now, list down the factors of 5355
:1,3,5,7,9,15,17,21,35,45,51,63,85,105,119,153,255,315,357,595,765,1071,1785,5355
Now, list down the factors of 3915
:1,3,5,9,15,27,29,45,87,135,145,261,435,783,1305,3915
Greatest Common Factor
We found the factors 5355,3915 . The biggest common factor number is the GCF number.
So the greatest common factor 5355,3915 is 45.
Lets's calculate LCM of 304,9584
| 2 | 304, 9584 |
| 2 | 152, 4792 |
| 2 | 76, 2396 |
| 2 | 38, 1198 |
| 19, 599 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 19 x 599 = 182096
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/182096
Therefore, the GCF of Fractions 5355/304,3915/9584 is 45/182096
Least Common Multiple of 304,9584 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 304,9584 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(304,9584) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(304,9584) x common factors =16 x 1 = 16
LCM(304,9584) = ( 304 × 9584 ) / 16
LCM(304,9584) = 2913536 / 16
LCM(304,9584) = 182096
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FAQs on GCF of Fractions of 5355/304, 3915/9584
1. What is the HCF of 5355,3915?
The HCF of 5355,3915 is 45
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 5355/304, 3915/9584?
Answer: GCF of Numerators as per given numbers 5355/304, 3915/9584 is
GCF of Numerators i.e. for 5355,3915 is 45
LCM of denominators i.e. for 304,9584 is 182096.
Thus, GCF of Fractions is 45/182096.Finally, GCF of Fractions for 5355/304, 3915/9584 is 45/182096.