102164400 has 360 divisors, whose sum is σ = 398776560. Its totient is φ = 24053760.

The previous prime is 102164399. The next prime is 102164401. The reversal of 102164400 is 4461201.

102164400 = T₁₄₉ + T₁₅₀ + ... + T₈₅₀.

102164400 is a `hidden beast` number, since 1 + 0 + 21 + 644 + 0 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (102164399) and next prime (102164401).

It is a tau number, because it is divible by the number of its divisors (360).

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

It is not an unprimeable number, because it can be changed into a prime (102164401) by changing a digit.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 1731571 + ... + 1731629.

Almost surely, 2^102164400 is an apocalyptic number.

102164400 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 102164400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (199388280).

102164400 is an abundant number, since it is smaller than the sum of its proper divisors (296612160).

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

102164400 is a wasteful number, since it uses less digits than its factorization.

102164400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 133 (or 119 counting only the distinct ones).

The product of its (nonzero) digits is 192, while the sum is 18.

The square root of 102164400 is about 10107.6406742622. The cubic root of 102164400 is about 467.4837612440.

The spelling of 102164400 in words is "one hundred two million, one hundred sixty-four thousand, four hundred".