75384000 has 224 divisors, whose sum is σ = 277368000. Its totient is φ = 20044800.

The previous prime is 75383993. The next prime is 75384007. The reversal of 75384000 is 48357.

75384000 = T₄₇₅ + T₄₇₆ + ... + T₈₂₃.

It is an interprime number because it is at equal distance from previous prime (75383993) and next prime (75384007).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (75384007) by changing a digit.

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 31 ways as a sum of consecutive naturals, for example, 215826 + ... + 216174.

It is an arithmetic number, because the mean of its divisors is an integer number (1238250).

Almost surely, 2^75384000 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 75384000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (138684000).

75384000 is an abundant number, since it is smaller than the sum of its proper divisors (201984000).

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

75384000 is a wasteful number, since it uses less digits than its factorization.

75384000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 385 (or 359 counting only the distinct ones).

The product of its (nonzero) digits is 3360, while the sum is 27.

The square root of 75384000 is about 8682.3959826767. The cubic root of 75384000 is about 422.4348370028.

The spelling of 75384000 in words is "seventy-five million, three hundred eighty-four thousand".