456676704000 has 1728 divisors, whose sum is σ = 1963845112320. Its totient is φ = 104509440000.

The previous prime is 456676703933. The next prime is 456676704007. The reversal of 456676704000 is 407676654.

It is a happy number.

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

It is a super-2 number, since 2×456676704000² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (456676704007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 1625183860 + ... + 1625184140.

It is an arithmetic number, because the mean of its divisors is an integer number (1136484440).

Almost surely, 2^456676704000 is an apocalyptic number.

456676704000 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 456676704000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (981922556160).

456676704000 is an abundant number, since it is smaller than the sum of its proper divisors (1507168408320).

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

456676704000 is a wasteful number, since it uses less digits than its factorization.

456676704000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 357 (or 321 counting only the distinct ones).

The product of its (nonzero) digits is 846720, while the sum is 45.

The spelling of 456676704000 in words is "four hundred fifty-six billion, six hundred seventy-six million, seven hundred four thousand".