The prime factorization of 54000 is 2 4×3 3×5 3.
How many positive integer factors (includes composite and prime) does 54000 have?
54000 has 80 factors.
Here is how the number of factors were calculated:
//In the future enter php code here to demonstrate how to find the number of factors.
The power factor one-dimensional arrays are:
Powers of 2: Array
(
[0] => 1
[1] => 2
[2] => 4
[3] => 8
[4] => 16
)
Powers of 3: Array
(
[0] => 1
[1] => 3
[2] => 9
[3] => 27
)
Powers of 5: Array
(
[0] => 1
[1] => 5
[2] => 25
[3] => 125
)
The 80 composite factors of 54000 are listed in the array below:
Array
(
[0] => Array
(
[0] => Array
(
[0] => 1
[1] => 5
[2] => 25
[3] => 125
)
[1] => Array
(
[0] => 3
[1] => 15
[2] => 75
[3] => 375
)
[2] => Array
(
[0] => 9
[1] => 45
[2] => 225
[3] => 1125
)
[3] => Array
(
[0] => 27
[1] => 135
[2] => 675
[3] => 3375
)
)
[1] => Array
(
[0] => Array
(
[0] => 2
[1] => 10
[2] => 50
[3] => 250
)
[1] => Array
(
[0] => 6
[1] => 30
[2] => 150
[3] => 750
)
[2] => Array
(
[0] => 18
[1] => 90
[2] => 450
[3] => 2250
)
[3] => Array
(
[0] => 54
[1] => 270
[2] => 1350
[3] => 6750
)
)
[2] => Array
(
[0] => Array
(
[0] => 4
[1] => 20
[2] => 100
[3] => 500
)
[1] => Array
(
[0] => 12
[1] => 60
[2] => 300
[3] => 1500
)
[2] => Array
(
[0] => 36
[1] => 180
[2] => 900
[3] => 4500
)
[3] => Array
(
[0] => 108
[1] => 540
[2] => 2700
[3] => 13500
)
)
[3] => Array
(
[0] => Array
(
[0] => 8
[1] => 40
[2] => 200
[3] => 1000
)
[1] => Array
(
[0] => 24
[1] => 120
[2] => 600
[3] => 3000
)
[2] => Array
(
[0] => 72
[1] => 360
[2] => 1800
[3] => 9000
)
[3] => Array
(
[0] => 216
[1] => 1080
[2] => 5400
[3] => 27000
)
)
[4] => Array
(
[0] => Array
(
[0] => 16
[1] => 80
[2] => 400
[3] => 2000
)
[1] => Array
(
[0] => 48
[1] => 240
[2] => 1200
[3] => 6000
)
[2] => Array
(
[0] => 144
[1] => 720
[2] => 3600
[3] => 18000
)
[3] => Array
(
[0] => 432
[1] => 2160
[2] => 10800
[3] => 54000
)
)
)
The composite factors listed in the array above are:
1 5 25 125 3 15 75 375 9 45 225 1125 27 135 675 3375 2 10 50 250 6 30 150 750 18 90 450 2250 54 270 1350 6750 4 20 100 500 12 60 300 1500 36 180 900 4500 108 540 2700 13500 8 40 200 1000 24 120 600 3000 72 360 1800 9000 216 1080 5400 27000 16 80 400 2000 48 240 1200 6000 144 720 3600 18000 432 2160 10800 54000