213504 has 40 divisors (see below), whose sum is σ = 572880. Its totient is φ = 70656.

The previous prime is 213491. The next prime is 213523. The reversal of 213504 is 405312.

213504 = 150² + 151² + ... + 158².

It is a nialpdrome in base 8.

It is an unprimeable number.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 1467 + ... + 1605.

It is an arithmetic number, because the mean of its divisors is an integer number (14322).

2²¹³⁵⁰⁴ is an apocalyptic number.

213504 is a gapful number since it is divisible by the number (24) 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 213504, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (286440).

213504 is an abundant number, since it is smaller than the sum of its proper divisors (359376).

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

213504 is an equidigital number, since it uses as much as digits as its factorization.

213504 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 160 (or 144 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 15.

The square root of 213504 is about 462.0649305022. The cubic root of 213504 is about 59.7679929238.

Adding to 213504 its reverse (405312), we get a palindrome (618816).

It can be divided in two parts, 213 and 504, that added together give a palindrome (717).

The spelling of 213504 in words is "two hundred thirteen thousand, five hundred four".