456782400 has 126 divisors (see below), whose sum is σ = 1623563682. Its totient is φ = 121804800.

The previous prime is 456782383. The next prime is 456782429. The reversal of 456782400 is 4287654.

It can be written as a sum of positive squares in 3 ways, for example, as 1557504 + 455224896 = 1248^2 + 21336^2 .

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

It is an unprimeable number.

It is a polite number, since it can be written in 17 ways as a sum of consecutive naturals, for example, 1461 + ... + 30260.

Almost surely, 2^456782400 is an apocalyptic number.

456782400 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 456782400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (811781841).

456782400 is an abundant number, since it is smaller than the sum of its proper divisors (1166781282).

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

456782400 is a wasteful number, since it uses less digits than its factorization.

456782400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 31749 (or 31731 counting only the distinct ones).

The product of its (nonzero) digits is 53760, while the sum is 36.

The square root of 456782400 is about 21372.4682711193. The cubic root of 456782400 is about 770.1401892386.

The spelling of 456782400 in words is "four hundred fifty-six million, seven hundred eighty-two thousand, four hundred".