GCF of 5460/340, 8640/1345
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5460/340, 8640/1345 i.e 60/91460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5460/340, 8640/1345.
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 5460/340,8640/1345?
Given fractions are 5460/340,8640/1345
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 5460/340,8640/1345, numerators are 5460,8640
Denominators are 340,1345
The GCF of 5460,8640 is 60 .
LCM of 340,1345 is 91460.
The greatest common factor of 5460/340,8640/1345 = [GCF of 5460,8640]/[LCM of 340,1345]= 60/91460
Therefore, the GCF of 5460/340,8640/1345 is 60/91460.
To find the highest common factor of 5460,8640, we have to find the factors of both numbers and list the highest common factor.
The factors of 5460 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 13, 14, 15, 20, 21, 26, 28, 30, 35, 39, 42, 52, 60, 65, 70, 78, 84, 91, 105, 130, 140, 156, 182, 195, 210, 260, 273, 364, 390, 420, 455, 546, 780, 910, 1092, 1365, 1820, 2730, 5460
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 5460,8640 is 60.
Lets's calculate GCF of 5460,8640
| 2 | 5460, 8640 |
| 2 | 2730, 4320 |
| 3 | 1365, 2160 |
| 5 | 455, 720 |
| 91, 144 |
∴ So the GCF of the given numbers is 2 x 2 x 3 x 5 = 60
Greatest Common Factor of 5460,8640 By Matching Biggest Common Factor Method
Now, list down the factors of 5460
:1,2,3,4,5,6,7,10,12,13,14,15,20,21,26,28,30,35,39,42,52,60,65,70,78,84,91,105,130,140,156,182,195,210,260,273,364,390,420,455,546,780,910,1092,1365,1820,2730,5460
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 5460,8640 . The biggest common factor number is the GCF number.
So the greatest common factor 5460,8640 is 60.
Lets's calculate LCM of 340,1345
| 5 | 340, 1345 |
| 68, 269 |
∴ So the LCM of the given numbers is 5 x 68 x 269 = 91460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 60/91460
Therefore, the GCF of Fractions 5460/340,8640/1345 is 60/91460
Least Common Multiple of 340,1345 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 340,1345 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(340,1345) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(340,1345) x common factors =5 x 1 = 5
LCM(340,1345) = ( 340 × 1345 ) / 5
LCM(340,1345) = 457300 / 5
LCM(340,1345) = 91460
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FAQs on GCF of Fractions of 5460/340, 8640/1345
1. What is the HCF of 5460,8640?
The HCF of 5460,8640 is 60
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 5460/340, 8640/1345?
Answer: GCF of Numerators as per given numbers 5460/340, 8640/1345 is
GCF of Numerators i.e. for 5460,8640 is 60
LCM of denominators i.e. for 340,1345 is 91460.
Thus, GCF of Fractions is 60/91460.Finally, GCF of Fractions for 5460/340, 8640/1345 is 60/91460.