7638400 has 192 divisors, whose sum is σ = 24284160. Its totient is φ = 2304000.

The previous prime is 7638383. The next prime is 7638401. The reversal of 7638400 is 48367.

7638400 is digitally balanced in base 5, because in such base it contains all the possibile digits an equal number of times.

It is a Harshad number since it is a multiple of its sum of digits (28).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (7638401) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 246385 + ... + 246415.

It is an arithmetic number, because the mean of its divisors is an integer number (126480).

Almost surely, 2^7638400 is an apocalyptic number.

7638400 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 7638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (12142080).

7638400 is an abundant number, since it is smaller than the sum of its proper divisors (16645760).

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

7638400 is a wasteful number, since it uses less digits than its factorization.

7638400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 73 (or 56 counting only the distinct ones).

The product of its (nonzero) digits is 4032, while the sum is 28.

The square root of 7638400 is about 2763.7655472200. The cubic root of 7638400 is about 196.9400901767.

The spelling of 7638400 in words is "seven million, six hundred thirty-eight thousand, four hundred".