33630 has 32 divisors (see below), whose sum is σ = 86400. Its totient is φ = 8352.

The previous prime is 33629. The next prime is 33637. The reversal of 33630 is 3633.

33630 = 80² + 81² + ... + 84².

33630 is digitally balanced in base 2 and base 4, because in such bases it contains all the possibile digits an equal number of times.

It is a super-2 number, since 2×33630² = 2261953800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a Curzon number.

It is a plaindrome in base 13.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (33637) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 541 + ... + 599.

It is an arithmetic number, because the mean of its divisors is an integer number (2700).

2³³⁶³⁰ is an apocalyptic number.

33630 is a gapful number since it is divisible by the number (30) formed by its first and last digit.

It is a practical number, because each smaller number is the sum of distinct divisors of 33630, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (43200).

33630 is an abundant number, since it is smaller than the sum of its proper divisors (52770).

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

33630 is a wasteful number, since it uses less digits than its factorization.

33630 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 88.

The product of its (nonzero) digits is 162, while the sum is 15.

The square root of 33630 is about 183.3848412492. The cubic root of 33630 is about 32.2781738056.

The spelling of 33630 in words is "thirty-three thousand, six hundred thirty".