464820314400 has 1008 divisors, whose sum is σ = 1882862317224. Its totient is φ = 111257763840.

The previous prime is 464820314351. The next prime is 464820314509. The reversal of 464820314400 is 4413028464.

464820314400 is a `hidden beast` number, since 4 + 6 + 4 + 8 + 203 + 1 + 440 + 0 = 666.

It can be written as a sum of positive squares in 12 ways, for example, as 16600776336 + 448219538064 = 128844^2 + 669492^2 .

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 167 ways as a sum of consecutive naturals, for example, 280518372 + ... + 280520028.

Almost surely, 2^464820314400 is an apocalyptic number.

464820314400 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 464820314400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (941431158612).

464820314400 is an abundant number, since it is smaller than the sum of its proper divisors (1418042002824).

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

464820314400 is a wasteful number, since it uses less digits than its factorization.

464820314400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1745 (or 1717 counting only the distinct ones).

The product of its (nonzero) digits is 73728, while the sum is 36.

The spelling of 464820314400 in words is "four hundred sixty-four billion, eight hundred twenty million, three hundred fourteen thousand, four hundred".