164400 has 60 divisors (see below), whose sum is σ = 530472. Its totient is φ = 43520.

The previous prime is 164387. The next prime is 164413. The reversal of 164400 is 4461.

It is an interprime number because it is at equal distance from previous prime (164387) and next prime (164413).

It is a tau number, because it is divible by the number of its divisors (60).

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

It is a self number, because there is not a number n which added to its sum of digits gives 164400.

It is an unprimeable number.

164400 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 1132 + ... + 1268.

2¹⁶⁴⁴⁰⁰ is an apocalyptic number.

164400 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 164400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (265236).

164400 is an abundant number, since it is smaller than the sum of its proper divisors (366072).

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

164400 is a wasteful number, since it uses less digits than its factorization.

164400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 158 (or 147 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 15.

The square root of 164400 is about 405.4626986543. The cubic root of 164400 is about 54.7815022726.

Adding to 164400 its reverse (4461), we get a palindrome (168861).

The spelling of 164400 in words is "one hundred sixty-four thousand, four hundred".