352512000 has 480 divisors, whose sum is σ = 1391349960. Its totient is φ = 88473600.

The previous prime is 352511993. The next prime is 352512029. The reversal of 352512000 is 215253.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 153363456 + 199148544 = 12384^2 + 14112^2 .

It is a tau number, because it is divible by the number of its divisors (480).

It is a hoax number, since the sum of its digits (18) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 20735992 + ... + 20736008.

Almost surely, 2^352512000 is an apocalyptic number.

352512000 is a gapful number since it is divisible by the number (30) 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 352512000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (695674980).

352512000 is an abundant number, since it is smaller than the sum of its proper divisors (1038837960).

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

352512000 is an equidigital number, since it uses as much as digits as its factorization.

352512000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 66 (or 27 counting only the distinct ones).

The product of its (nonzero) digits is 300, while the sum is 18.

The square root of 352512000 is about 18775.3029269836. The cubic root of 352512000 is about 706.4118380260.

Adding to 352512000 its reverse (215253), we get a palindrome (352727253).

The spelling of 352512000 in words is "three hundred fifty-two million, five hundred twelve thousand".