470705766400 has 207 divisors, whose sum is σ = 1185033345069. Its totient is φ = 185472122880.

The previous prime is 470705766389. The next prime is 470705766413. The reversal of 470705766400 is 4667507074.

The square root of 470705766400 is 686080.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in only one way, i.e., 169454075904 + 301251690496 = 411648^2 + 548864^2 .

It is a super-2 number, since 2×470705766400² (a number of 24 digits) contains 22 as substring.

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 7025459167 + ... + 7025459233.

Almost surely, 2^470705766400 is an apocalyptic number.

470705766400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

470705766400 is the 686080-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 470705766400

470705766400 is an abundant number, since it is smaller than the sum of its proper divisors (714327578669).

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

470705766400 is an frugal number, since it uses more digits than its factorization.

470705766400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 188 (or 74 counting only the distinct ones).

The product of its (nonzero) digits is 987840, while the sum is 46.

The spelling of 470705766400 in words is "four hundred seventy billion, seven hundred five million, seven hundred sixty-six thousand, four hundred".