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. |
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| 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 ).
Read more about this topic: Highly Composite Number
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