Highly Composite Number - Examples

Examples

The highly composite number : 10,080.
10,080 = (2 × 2 × 2 × 2 × 2) × (3 × 3) × 5 × 7
By (2) above, 10,080 has exactly seventy-two divisors.
1
×
10,080
2
×
5,040
3
×
3,360
4
×
2,520
5
×
2,016
6
×
1,680
7
×
1,440
8
×
1,260
9
×
1,120
10
×
1,008
12
×
840
14
×
720
15
×
672
16
×
630
18
×
560
20
×
504
21
×
480
24
×
420
28
×
360
30
×
336
32
×
315
35
×
288
36
×
280
40
×
252
42
×
240
45
×
224
48
×
210
56
×
180
60
×
168
63
×
160
70
×
144
72
×
140
80
×
126
84
×
120
90
×
112
96
×
105
Note: The bolded numbers are themselves highly composite numbers.
Only the twentieth highly composite number 7560 (= 3 × 2520) is absent.
10080 is a so-called 7-smooth number, (sequence A002473 in OEIS).

The 15,000th highly composite number can be found on Achim Flammenkamp's website. It is the product of 230 primes:

where is the sequence of successive prime numbers, and all omitted terms (a22 to a228) are factors with exponent equal to one (i.e. the number is ).

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