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prime factorizations of some small
highly composite numbers∗
PrimeFan†
2013-03-22 2:42:38
All highly composite numbers have prime factorizations containing consecutive prime numbers, starting with 2, while the exponents form a sequence in
descending order (the number 1 as an exponent is tacit in the following table).
∗ hPrimeFactorizationsOfSomeSmallHighlyCompositeNumbersi created: h2013-03-2i by:
hPrimeFani version: h41670i Privacy setting: h1i hExamplei h11N56i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
You can reuse this document or portions thereof only if you do so under terms that are
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1
HCN
4
6
12
24
36
48
60
120
180
240
360
720
840
1260
1680
2520
5040
7560
10080
15120
20160
25200
27720
45360
50400
55440
83160
110880
166320
221760
277200
332640
498960
554400
665280
720720
1081080
1441440
2162160
Factorization
22
2×3
22 × 3
23 × 3
22 × 32
24 × 3
22 × 3 × 5
23 × 3 × 5
22 × 32 × 5
24 × 3 × 5
23 × 32 × 5
24 × 32 × 5
23 × 3 × 5 × 7
22 × 32 × 5 × 7
24 × 3 × 5 × 7
23 × 32 × 5 × 7
24 × 32 × 5 × 7
23 × 33 × 5 × 7
25 × 32 × 5 × 7
24 × 33 × 5 × 7
26 × 32 × 5 × 7
24 × 32 × 52 × 7
23 × 32 × 5 × 7 × 11
24 × 34 × 5 × 7
25 × 32 × 52 × 7
24 × 32 × 5 × 7 × 11
23 × 33 × 5 × 7 × 11
25 × 32 × 5 × 7 × 11
24 × 33 × 5 × 7 × 11
26 × 32 × 5 × 7 × 11
24 × 32 × 52 × 7 × 11
25 × 33 × 5 × 7 × 11
24 × 34 × 5 × 7 × 11
25 × 32 × 52 × 7 × 11
26 × 33 × 5 × 7 × 11
24 × 32 × 5 × 7 × 11 × 13
23 × 33 × 5 × 7 × 11 × 13
25 × 32 × 5 × 7 × 11 × 13
24 × 33 × 5 × 7 × 11 × 13
2