164284800 has 192 divisors, whose sum is σ = 549555600. Its totient is φ = 43130880.

The previous prime is 164284781. The next prime is 164284819. The reversal of 164284800 is 8482461.

It is an interprime number because it is at equal distance from previous prime (164284781) and next prime (164284819).

It is a tau number, because it is divible by the number of its divisors (192).

It is a super-2 number, since 2×164284800² = 53978991022080000, which contains 22 as substring.

It is a hoax number, since the sum of its digits (33) coincides with the sum of the digits of its distinct prime factors.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1046322 + ... + 1046478.

Almost surely, 2^164284800 is an apocalyptic number.

164284800 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 164284800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (274777800).

164284800 is an abundant number, since it is smaller than the sum of its proper divisors (385270800).

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

164284800 is a wasteful number, since it uses less digits than its factorization.

164284800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 293 (or 276 counting only the distinct ones).

The product of its (nonzero) digits is 12288, while the sum is 33.

The square root of 164284800 is about 12817.3632233779. The cubic root of 164284800 is about 547.6870360332.

It can be divided in two parts, 16428 and 4800, that multiplied together give a square (78854400 = 8880²).

The spelling of 164284800 in words is "one hundred sixty-four million, two hundred eighty-four thousand, eight hundred".