GCF of 1542/406, 8640/5340
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1542/406, 8640/5340 i.e 6/1084020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1542/406, 8640/5340.
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 1542/406,8640/5340?
Given fractions are 1542/406,8640/5340
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 1542/406,8640/5340, numerators are 1542,8640
Denominators are 406,5340
The GCF of 1542,8640 is 6 .
LCM of 406,5340 is 1084020.
The greatest common factor of 1542/406,8640/5340 = [GCF of 1542,8640]/[LCM of 406,5340]= 6/1084020
Therefore, the GCF of 1542/406,8640/5340 is 6/1084020.
To find the highest common factor of 1542,8640, we have to find the factors of both numbers and list the highest common factor.
The factors of 1542 are 1, 2, 3, 6, 257, 514, 771, 1542
The factors of 8640 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 64, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 192, 216, 240, 270, 288, 320, 360, 432, 480, 540, 576, 720, 864, 960, 1080, 1440, 1728, 2160, 2880, 4320, 8640
The HCF of 1542,8640 is 6.
Lets's calculate GCF of 1542,8640
| 2 | 1542, 8640 |
| 3 | 771, 4320 |
| 257, 1440 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 1542,8640 By Matching Biggest Common Factor Method
Now, list down the factors of 1542
:1,2,3,6,257,514,771,1542
Now, list down the factors of 8640
:1,2,3,4,5,6,8,9,10,12,15,16,18,20,24,27,30,32,36,40,45,48,54,60,64,72,80,90,96,108,120,135,144,160,180,192,216,240,270,288,320,360,432,480,540,576,720,864,960,1080,1440,1728,2160,2880,4320,8640
Greatest Common Factor
We found the factors 1542,8640 . The biggest common factor number is the GCF number.
So the greatest common factor 1542,8640 is 6.
Lets's calculate LCM of 406,5340
| 2 | 406, 5340 |
| 203, 2670 |
∴ So the LCM of the given numbers is 2 x 203 x 2670 = 1084020
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1084020
Therefore, the GCF of Fractions 1542/406,8640/5340 is 6/1084020
Least Common Multiple of 406,5340 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 406,5340 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,5340) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(406,5340) x common factors =2 x 1 = 2
LCM(406,5340) = ( 406 × 5340 ) / 2
LCM(406,5340) = 2168040 / 2
LCM(406,5340) = 1084020
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 1542/406, 8640/5340
1. What is the HCF of 1542,8640?
The HCF of 1542,8640 is 6
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 1542/406, 8640/5340?
Answer: GCF of Numerators as per given numbers 1542/406, 8640/5340 is
GCF of Numerators i.e. for 1542,8640 is 6
LCM of denominators i.e. for 406,5340 is 1084020.
Thus, GCF of Fractions is 6/1084020.Finally, GCF of Fractions for 1542/406, 8640/5340 is 6/1084020.