45958784400 has 315 divisors, whose sum is σ = 165966286611. Its totient is φ = 12224805120.

The previous prime is 45958784393. The next prime is 45958784413. The reversal of 45958784400 is 448785954.

It is a happy number.

The square root of 45958784400 is 214380.

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

45958784400 is a `hidden beast` number, since 4 + 59 + 587 + 8 + 4 + 4 + 0 + 0 = 666.

45958784400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 4 ways, for example, as 46294416 + 45912489984 = 6804^2 + 214272^2 .

It is a super-2 number, since 2×45958784400² (a number of 22 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a polite number, since it can be written in 62 ways as a sum of consecutive naturals, for example, 115765002 + ... + 115765398.

Almost surely, 2^45958784400 is an apocalyptic number.

45958784400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

45958784400 is the 214380-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 45958784400

45958784400 is an abundant number, since it is smaller than the sum of its proper divisors (120007502211).

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

45958784400 is an frugal number, since it uses more digits than its factorization.

45958784400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 830 (or 407 counting only the distinct ones).

The product of its (nonzero) digits is 6451200, while the sum is 54.

The spelling of 45958784400 in words is "forty-five billion, nine hundred fifty-eight million, seven hundred eighty-four thousand, four hundred".