456686630400 has 1440 divisors, whose sum is σ = 2044334654208. Its totient is φ = 86792601600.

The previous prime is 456686630383. The next prime is 456686630471. The reversal of 456686630400 is 4036686654.

It is a super-2 number, since 2×456686630400² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 456686630400.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 4189785546 + ... + 4189785654.

Almost surely, 2^456686630400 is an apocalyptic number.

456686630400 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 456686630400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1022167327104).

456686630400 is an abundant number, since it is smaller than the sum of its proper divisors (1587648023808).

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

456686630400 is a wasteful number, since it uses less digits than its factorization.

456686630400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 280 (or 150 counting only the distinct ones).

The product of its (nonzero) digits is 2488320, while the sum is 48.

The spelling of 456686630400 in words is "four hundred fifty-six billion, six hundred eighty-six million, six hundred thirty thousand, four hundred".