# prime factorizations of some small highly composite numbers

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).

HCN Factorization
4 $2^{2}$
6 $2\times 3$
12 $2^{2}\times 3$
24 $2^{3}\times 3$
36 $2^{2}\times 3^{2}$
48 $2^{4}\times 3$
60 $2^{2}\times 3\times 5$
120 $2^{3}\times 3\times 5$
180 $2^{2}\times 3^{2}\times 5$
240 $2^{4}\times 3\times 5$
360 $2^{3}\times 3^{2}\times 5$
720 $2^{4}\times 3^{2}\times 5$
840 $2^{3}\times 3\times 5\times 7$
1260 $2^{2}\times 3^{2}\times 5\times 7$
1680 $2^{4}\times 3\times 5\times 7$
2520 $2^{3}\times 3^{2}\times 5\times 7$
5040 $2^{4}\times 3^{2}\times 5\times 7$
7560 $2^{3}\times 3^{3}\times 5\times 7$
10080 $2^{5}\times 3^{2}\times 5\times 7$
15120 $2^{4}\times 3^{3}\times 5\times 7$
20160 $2^{6}\times 3^{2}\times 5\times 7$
25200 $2^{4}\times 3^{2}\times 5^{2}\times 7$
27720 $2^{3}\times 3^{2}\times 5\times 7\times 11$
45360 $2^{4}\times 3^{4}\times 5\times 7$
50400 $2^{5}\times 3^{2}\times 5^{2}\times 7$
55440 $2^{4}\times 3^{2}\times 5\times 7\times 11$
83160 $2^{3}\times 3^{3}\times 5\times 7\times 11$
110880 $2^{5}\times 3^{2}\times 5\times 7\times 11$
166320 $2^{4}\times 3^{3}\times 5\times 7\times 11$
221760 $2^{6}\times 3^{2}\times 5\times 7\times 11$
277200 $2^{4}\times 3^{2}\times 5^{2}\times 7\times 11$
332640 $2^{5}\times 3^{3}\times 5\times 7\times 11$
498960 $2^{4}\times 3^{4}\times 5\times 7\times 11$
554400 $2^{5}\times 3^{2}\times 5^{2}\times 7\times 11$
665280 $2^{6}\times 3^{3}\times 5\times 7\times 11$
720720 $2^{4}\times 3^{2}\times 5\times 7\times 11\times 13$
1081080 $2^{3}\times 3^{3}\times 5\times 7\times 11\times 13$
1441440 $2^{5}\times 3^{2}\times 5\times 7\times 11\times 13$
2162160 $2^{4}\times 3^{3}\times 5\times 7\times 11\times 13$
Title prime factorizations of some small highly composite numbers PrimeFactorizationsOfSomeSmallHighlyCompositeNumbers 2013-03-22 18:51:29 2013-03-22 18:51:29 PrimeFan (13766) PrimeFan (13766) 5 PrimeFan (13766) Example msc 11N56