4638624000 has 288 divisors, whose sum is σ = 15547808640. Its totient is φ = 1225728000.

The previous prime is 4638623993. The next prime is 4638624007. The reversal of 4638624000 is 4268364.

It is an interprime number because it is at equal distance from previous prime (4638623993) and next prime (4638624007).

It is a super-2 number, since 2×4638624000² = 43033665226752000000, which contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (4638624007) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 20255886 + ... + 20256114.

Almost surely, 2^4638624000 is an apocalyptic number.

4638624000 is a gapful number since it is divisible by the number (40) 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 4638624000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (7773904320).

4638624000 is an abundant number, since it is smaller than the sum of its proper divisors (10909184640).

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

4638624000 is a wasteful number, since it uses less digits than its factorization.

4638624000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 474 (or 450 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 33.

The square root of 4638624000 is about 68107.4445270119. Note that the first 3 decimals coincide. The cubic root of 4638624000 is about 1667.7452928998.

The spelling of 4638624000 in words is "four billion, six hundred thirty-eight million, six hundred twenty-four thousand".