352800 has 162 divisors, whose sum is σ = 1447173. Its totient is φ = 80640.

The previous prime is 352771. The next prime is 352813. The reversal of 352800 is 8253.

352800 = T₃₁ + T₃₂ + ... + T₁₂₈.

352800 = 21³ + 22³ + ... + 35³.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in 2 ways, for example, as 345744 + 7056 = 588^2 + 84^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=420.

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

It is an Ulam number.

It is an unprimeable number.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 50397 + ... + 50403.

2³⁵²⁸⁰⁰ is an apocalyptic number.

352800 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 352800

352800 is an abundant number, since it is smaller than the sum of its proper divisors (1094373).

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

352800 is a wasteful number, since it uses less digits than its factorization.

352800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 40 (or 17 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 352800 is about 593.9696961967. The cubic root of 352800 is about 70.6604163611.

Multiplying 352800 by its sum of digits (18), we get a square (6350400 = 2520²).

352800 divided by its sum of digits (18) gives a square (19600 = 140²).

The spelling of 352800 in words is "three hundred fifty-two thousand, eight hundred".