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Highly composite numbers (view source)
Revision as of 07:28, January 15, 2017
, 07:28, January 15, 2017this is the earlier page, namely the one to which the prime number page did not link. The prime number page linked only to the composite number page. And the prime number page confounded the term 'highly composite' with 'composite'
On the opposite extreme from the primes are the '''highly composite numbers'''. The primes have the least quantity of factors, namely two. A highly composite number is one which has a greater number of factors than any smaller number. In other words, the highly composite numbers each '''''initiate''''' an ''increase'' in quantity of factors over that of any lesser number.
On the opposite extreme from a [[prime]] number is a '''highly composite number'''. A prime has the least quantity of factors, namely two. A highly composite number is one which has a greater number of factors than any smaller number. In other words, a highly composite number '''''initiates''''' an ''increase'' in quantity of factors over that of any lesser number.
For example, 180 has more factors than any smaller number, or any greater one up to 240. Then, 240 has an additional two more factors than 180. Then, no number above 240 has more factors than 240, until you get to 360, while the quantity of factors of 336 merely ''equals'' that of 240.
For example, 120 has more factors than any smaller number, and also has more factors than numbers lesser than 180. 180, in turn, has an additional two more factors than 120. And 180 has more factors than numbers less than 240. And 240 has more factors than numbers lesser than 360.
Additionally, the unifying number for all highly composite numbers is 12. This is because of three facts:
Additionally, the unifying number for all highly composite numbers is 12. This is because of three facts: