1353590400 has 384 divisors, whose sum is σ = 4834065600. Its totient is φ = 331776000.

The previous prime is 1353590389. The next prime is 1353590423. The reversal of 1353590400 is 40953531.

It is a tau number, because it is divible by the number of its divisors (384).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 7478310 + ... + 7478490.

Almost surely, 2^1353590400 is an apocalyptic number.

1353590400 is a gapful number since it is divisible by the number (10) 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 1353590400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2417032800).

1353590400 is an abundant number, since it is smaller than the sum of its proper divisors (3480475200).

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

1353590400 is a wasteful number, since it uses less digits than its factorization.

1353590400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 268 (or 251 counting only the distinct ones).

The product of its (nonzero) digits is 8100, while the sum is 30.

The square root of 1353590400 is about 36791.1728543682. The cubic root of 1353590400 is about 1106.1883709164.

The spelling of 1353590400 in words is "one billion, three hundred fifty-three million, five hundred ninety thousand, four hundred".