409968000 has 512 divisors, whose sum is σ = 1648483200. Its totient is φ = 99532800.

The previous prime is 409967969. The next prime is 409968011. The reversal of 409968000 is 869904.

It is a super-2 number, since 2×409968000² = 336147522048000000, which contains 22 as substring.

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 5615964 + ... + 5616036.

Almost surely, 2^409968000 is an apocalyptic number.

409968000 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 409968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (824241600).

409968000 is an abundant number, since it is smaller than the sum of its proper divisors (1238515200).

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

409968000 is a wasteful number, since it uses less digits than its factorization.

409968000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 124 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 15552, while the sum is 36.

The square root of 409968000 is about 20247.6665322204. Note that the first 3 decimals coincide. The cubic root of 409968000 is about 742.8765562692.

The spelling of 409968000 in words is "four hundred nine million, nine hundred sixty-eight thousand".