105264000 has 384 divisors, whose sum is σ = 409574880. Its totient is φ = 25804800.

The previous prime is 105263999. The next prime is 105264013. The reversal of 105264000 is 462501.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (384).

It is a super-2 number, since 2×105264000² = 22161019392000000, which contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 2447979 + ... + 2448021.

Almost surely, 2^105264000 is an apocalyptic number.

105264000 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 105264000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (204787440).

105264000 is an abundant number, since it is smaller than the sum of its proper divisors (304310880).

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

105264000 is a wasteful number, since it uses less digits than its factorization.

105264000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 95 (or 70 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 105264000 is about 10259.8245599035. The cubic root of 105264000 is about 472.1644548072.

The spelling of 105264000 in words is "one hundred five million, two hundred sixty-four thousand".