408848400 has 135 divisors (see below), whose sum is σ = 1423040151. Its totient is φ = 108702720.

The previous prime is 408848393. The next prime is 408848417. The reversal of 408848400 is 4848804.

The square root of 408848400 is 20220.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 4 ways, for example, as 56610576 + 352237824 = 7524^2 + 18768^2 .

It is a super-3 number, since 3×408848400³ (a number of 27 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 1213032 + ... + 1213368.

Almost surely, 2^408848400 is an apocalyptic number.

408848400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

408848400 is the 20220-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 408848400

408848400 is an abundant number, since it is smaller than the sum of its proper divisors (1014191751).

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

408848400 is a wasteful number, since it uses less digits than its factorization.

408848400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 698 (or 347 counting only the distinct ones).

The product of its (nonzero) digits is 32768, while the sum is 36.

The cubic root of 408848400 is about 742.1996880953.

Multiplying 408848400 by its sum of digits (36), we get a square (14718542400 = 121320²).

408848400 divided by its sum of digits (36) gives a square (11356900 = 3370²).

It can be divided in two parts, 40884 and 8400, that added together give a square (49284 = 222²).

The spelling of 408848400 in words is "four hundred eight million, eight hundred forty-eight thousand, four hundred".