7525638400 has 216 divisors, whose sum is σ = 21433253184. Its totient is φ = 2562662400.

The previous prime is 7525638361. The next prime is 7525638413. The reversal of 7525638400 is 48365257.

It is a Harshad number since it is a multiple of its sum of digits (40).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 7749915 + ... + 7750885.

It is an arithmetic number, because the mean of its divisors is an integer number (99228024).

Almost surely, 2^7525638400 is an apocalyptic number.

7525638400 is a gapful number since it is divisible by the number (70) 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 7525638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (10716626592).

7525638400 is an abundant number, since it is smaller than the sum of its proper divisors (13907614784).

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

7525638400 is a wasteful number, since it uses less digits than its factorization.

7525638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1177 (or 1158 counting only the distinct ones).

The product of its (nonzero) digits is 201600, while the sum is 40.

The square root of 7525638400 is about 86750.4374628739. The cubic root of 7525638400 is about 1959.6617492092.

The spelling of 7525638400 in words is "seven billion, five hundred twenty-five million, six hundred thirty-eight thousand, four hundred".