638400 has 168 divisors, whose sum is σ = 2519680. Its totient is φ = 138240.

The previous prime is 638371. The next prime is 638423. The reversal of 638400 is 4836.

638400 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a Cunningham number, because it is equal to 799²-1.

It is a tau number, because it is divible by the number of its divisors (168).

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a congruent number.

It is an unprimeable number.

638400 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 33591 + ... + 33609.

2⁶³⁸⁴⁰⁰ is an apocalyptic number.

638400 is a gapful number since it is divisible by the number (60) 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 638400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1259840).

638400 is an abundant number, since it is smaller than the sum of its proper divisors (1881280).

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

638400 is a wasteful number, since it uses less digits than its factorization.

638400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 51 (or 36 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 21.

The square root of 638400 is about 798.9993742175. Note that the first 3 decimals coincide. The cubic root of 638400 is about 86.1055131829.

It can be divided in two parts, 6 and 38400, that multiplied together give a square (230400 = 480²).

The spelling of 638400 in words is "six hundred thirty-eight thousand, four hundred".