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2520
2520 superior highly composite number; smallest number divisible by numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 12 ; colossally abundant number; Harshad number in several bases. It is also the highest number with more divisors than any number less than double itself.(sequence A072938 in OEIS) Not only is it the 7th (and last) number with more divisors than any number double itself but it also the 7th number that is highly composite and the lowest common multiple of a consecutive set of integers from 1 (sequence A095921 in OEIS) which is a property the previous number with this pattern of divisors does not have (360). That is, although 360 and 2520 both have more divisors than any number twice themselves, 2520 is the lowest number divisible by both 1 to 9 and 1 to 10, whereas 360 is not the lowest number divisible by 1 to 6 (which 60 is) and is not divisible by 1 to 7 (which 420 is). It is also the 6th and largest highly composite number that is a divisor of every higher highly composite number.(sequence A106037 in OEIS)
2520 is the smallest number divisible by all integers from 1 to 10, i.e., it is their least common multiple.
2520 is half of 7! (5040), meaning 7 factorial, or 1×2×3×4×5×6×7.
2520 is the product of five consecutive numbers, namely 3×4×5×6×7.
2520 is a superior highly composite number.
2520 is a colossally abundant number.
2520 is the last highly composite number which is half of the next highly composite number.[1]
2520 is the last highly composite number that is a divisor of all following highly composite numbers.[2]
Factors
The factors, also called divisors, of 2520 are the following:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260, 2520.[3]
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References
http://oeis.org/A072938
http://oeis.org/A106037
http://numberworld.info/2520
