GCF of 1984/469, 5760/4810
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1984/469, 5760/4810 i.e 64/2255890 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1984/469, 5760/4810.
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 1984/469,5760/4810?
Given fractions are 1984/469,5760/4810
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 1984/469,5760/4810, numerators are 1984,5760
Denominators are 469,4810
The GCF of 1984,5760 is 64 .
LCM of 469,4810 is 2255890.
The greatest common factor of 1984/469,5760/4810 = [GCF of 1984,5760]/[LCM of 469,4810]= 64/2255890
Therefore, the GCF of 1984/469,5760/4810 is 64/2255890.
To find the highest common factor of 1984,5760, we have to find the factors of both numbers and list the highest common factor.
The factors of 1984 are 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984
The factors of 5760 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 64, 72, 80, 90, 96, 120, 128, 144, 160, 180, 192, 240, 288, 320, 360, 384, 480, 576, 640, 720, 960, 1152, 1440, 1920, 2880, 5760
The HCF of 1984,5760 is 64.
Lets's calculate GCF of 1984,5760
| 2 | 1984, 5760 |
| 2 | 992, 2880 |
| 2 | 496, 1440 |
| 2 | 248, 720 |
| 2 | 124, 360 |
| 2 | 62, 180 |
| 31, 90 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 = 64
Greatest Common Factor of 1984,5760 By Matching Biggest Common Factor Method
Now, list down the factors of 1984
:1,2,4,8,16,31,32,62,64,124,248,496,992,1984
Now, list down the factors of 5760
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,30,32,36,40,45,48,60,64,72,80,90,96,120,128,144,160,180,192,240,288,320,360,384,480,576,640,720,960,1152,1440,1920,2880,5760
Greatest Common Factor
We found the factors 1984,5760 . The biggest common factor number is the GCF number.
So the greatest common factor 1984,5760 is 64.
Lets's calculate LCM of 469,4810
Given numbers has no common factors except 1. So, there LCM is their product i.e 2255890
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 64/2255890
Therefore, the GCF of Fractions 1984/469,5760/4810 is 64/2255890
Least Common Multiple of 469,4810 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 469,4810 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(469,4810) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(469,4810) x common factors =1 x 1 = 1
LCM(469,4810) = ( 469 × 4810 ) / 1
LCM(469,4810) = 2255890 / 1
LCM(469,4810) = 2255890
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FAQs on GCF of Fractions of 1984/469, 5760/4810
1. What is the HCF of 1984,5760?
The HCF of 1984,5760 is 64
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 1984/469, 5760/4810?
Answer: GCF of Numerators as per given numbers 1984/469, 5760/4810 is
GCF of Numerators i.e. for 1984,5760 is 64
LCM of denominators i.e. for 469,4810 is 2255890.
Thus, GCF of Fractions is 64/2255890.Finally, GCF of Fractions for 1984/469, 5760/4810 is 64/2255890.