407579040 has 288 divisors, whose sum is σ = 1575153216. Its totient is φ = 98703360.

The previous prime is 407579017. The next prime is 407579047. The reversal of 407579040 is 40975704.

It is a happy number.

407579040 is a `hidden beast` number, since 40 + 7 + 579 + 0 + 40 = 666.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-3 number, since 3×407579040³ (a number of 27 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 407578986 and 407579004.

It is not an unprimeable number, because it can be changed into a prime (407579047) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 427204 + ... + 428156.

It is an arithmetic number, because the mean of its divisors is an integer number (5469282).

Almost surely, 2^407579040 is an apocalyptic number.

407579040 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 407579040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (787576608).

407579040 is an abundant number, since it is smaller than the sum of its proper divisors (1167574176).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

407579040 is a wasteful number, since it uses less digits than its factorization.

407579040 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 994 (or 974 counting only the distinct ones).

The product of its (nonzero) digits is 35280, while the sum is 36.

The square root of 407579040 is about 20188.5868747666. The cubic root of 407579040 is about 741.4307842781.

The spelling of 407579040 in words is "four hundred seven million, five hundred seventy-nine thousand, forty".