The prime factorization of 21600 is 2 5×3 3×5 2.
How many positive integer factors (includes composite and prime) does 21600 have?
21600 has 72 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
[5] => 32
)
Powers of 3: Array
(
[0] => 1
[1] => 3
[2] => 9
[3] => 27
)
Powers of 5: Array
(
[0] => 1
[1] => 5
[2] => 25
)
The 72 composite factors of 21600 are listed in the array below:
Array
(
[0] => Array
(
[0] => Array
(
[0] => 1
[1] => 5
[2] => 25
)
[1] => Array
(
[0] => 3
[1] => 15
[2] => 75
)
[2] => Array
(
[0] => 9
[1] => 45
[2] => 225
)
[3] => Array
(
[0] => 27
[1] => 135
[2] => 675
)
)
[1] => Array
(
[0] => Array
(
[0] => 2
[1] => 10
[2] => 50
)
[1] => Array
(
[0] => 6
[1] => 30
[2] => 150
)
[2] => Array
(
[0] => 18
[1] => 90
[2] => 450
)
[3] => Array
(
[0] => 54
[1] => 270
[2] => 1350
)
)
[2] => Array
(
[0] => Array
(
[0] => 4
[1] => 20
[2] => 100
)
[1] => Array
(
[0] => 12
[1] => 60
[2] => 300
)
[2] => Array
(
[0] => 36
[1] => 180
[2] => 900
)
[3] => Array
(
[0] => 108
[1] => 540
[2] => 2700
)
)
[3] => Array
(
[0] => Array
(
[0] => 8
[1] => 40
[2] => 200
)
[1] => Array
(
[0] => 24
[1] => 120
[2] => 600
)
[2] => Array
(
[0] => 72
[1] => 360
[2] => 1800
)
[3] => Array
(
[0] => 216
[1] => 1080
[2] => 5400
)
)
[4] => Array
(
[0] => Array
(
[0] => 16
[1] => 80
[2] => 400
)
[1] => Array
(
[0] => 48
[1] => 240
[2] => 1200
)
[2] => Array
(
[0] => 144
[1] => 720
[2] => 3600
)
[3] => Array
(
[0] => 432
[1] => 2160
[2] => 10800
)
)
[5] => Array
(
[0] => Array
(
[0] => 32
[1] => 160
[2] => 800
)
[1] => Array
(
[0] => 96
[1] => 480
[2] => 2400
)
[2] => Array
(
[0] => 288
[1] => 1440
[2] => 7200
)
[3] => Array
(
[0] => 864
[1] => 4320
[2] => 21600
)
)
)
The composite factors listed in the array above are:
1 5 25 3 15 75 9 45 225 27 135 675 2 10 50 6 30 150 18 90 450 54 270 1350 4 20 100 12 60 300 36 180 900 108 540 2700 8 40 200 24 120 600 72 360 1800 216 1080 5400 16 80 400 48 240 1200 144 720 3600 432 2160 10800 32 160 800 96 480 2400 288 1440 7200 864 4320 21600