814000928400 has 405 divisors, whose sum is σ = 3107228739433. Its totient is φ = 197189203200.

The previous prime is 814000928359. The next prime is 814000928431. The reversal of 814000928400 is 4829000418.

The square root of 814000928400 is 902220.

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

814000928400 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in only one way, i.e., 293040334224 + 520960594176 = 541332^2 + 721776^2 .

It is a super-2 number, since 2×814000928400² (a number of 25 digits) contains 22 as substring.

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

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 595464517 + ... + 595465883.

Almost surely, 2^814000928400 is an apocalyptic number.

814000928400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

814000928400 is the 902220-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 814000928400

814000928400 is an abundant number, since it is smaller than the sum of its proper divisors (2293227811033).

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

814000928400 is a wasteful number, since it uses less digits than its factorization.

814000928400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2780 (or 1388 counting only the distinct ones).

The product of its (nonzero) digits is 18432, while the sum is 36.

Multiplying 814000928400 by its sum of digits (36), we get a square (29304033422400 = 5413320²).

814000928400 divided by its sum of digits (36) gives a square (22611136900 = 150370²).

Adding to 814000928400 its reverse (4829000418), we get a palindrome (818829928818).

It can be divided in two parts, 814000 and 928400, that added together give a square (1742400 = 1320²).

The spelling of 814000928400 in words is "eight hundred fourteen billion, nine hundred twenty-eight thousand, four hundred".