prime factorizations of some small highly composite numbers


All highly composite numbers have prime factorizationsMathworldPlanetmath containing consecutive prime numbersMathworldPlanetmath, starting with 2, while the exponents form a sequence in descending orderPlanetmathPlanetmath (the number 1 as an exponent is tacit in the following table).

HCN Factorization
4 22
6 2×3
12 22×3
24 23×3
36 22×32
48 24×3
60 22×3×5
120 23×3×5
180 22×32×5
240 24×3×5
360 23×32×5
720 24×32×5
840 23×3×5×7
1260 22×32×5×7
1680 24×3×5×7
2520 23×32×5×7
5040 24×32×5×7
7560 23×33×5×7
10080 25×32×5×7
15120 24×33×5×7
20160 26×32×5×7
25200 24×32×52×7
27720 23×32×5×7×11
45360 24×34×5×7
50400 25×32×52×7
55440 24×32×5×7×11
83160 23×33×5×7×11
110880 25×32×5×7×11
166320 24×33×5×7×11
221760 26×32×5×7×11
277200 24×32×52×7×11
332640 25×33×5×7×11
498960 24×34×5×7×11
554400 25×32×52×7×11
665280 26×33×5×7×11
720720 24×32×5×7×11×13
1081080 23×33×5×7×11×13
1441440 25×32×5×7×11×13
2162160 24×33×5×7×11×13
Title prime factorizations of some small highly composite numbers
Canonical name PrimeFactorizationsOfSomeSmallHighlyCompositeNumbers
Date of creation 2013-03-22 18:51:29
Last modified on 2013-03-22 18:51:29
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 5
Author PrimeFan (13766)
Entry type Example
Classification msc 11N56