407904456960 has 1728 divisors, whose sum is σ = 1956321884160. Its totient is φ = 78153154560.

The previous prime is 407904456931. The next prime is 407904456997. The reversal of 407904456960 is 69654409704.

It is a happy number.

407904456960 is a `hidden beast` number, since 4 + 0 + 79 + 0 + 4 + 4 + 569 + 6 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1728).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a junction number, because it is equal to n+sod(n) for n = 407904456897 and 407904456906.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 449728827 + ... + 449729733.

It is an arithmetic number, because the mean of its divisors is an integer number (1132130720).

Almost surely, 2^407904456960 is an apocalyptic number.

407904456960 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 407904456960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (978160942080).

407904456960 is an abundant number, since it is smaller than the sum of its proper divisors (1548417427200).

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

407904456960 is a wasteful number, since it uses less digits than its factorization.

407904456960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 981 (or 948 counting only the distinct ones).

The product of its (nonzero) digits is 6531840, while the sum is 54.

The spelling of 407904456960 in words is "four hundred seven billion, nine hundred four million, four hundred fifty-six thousand, nine hundred sixty".