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
Famous quotes containing the word examples:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)