413744000 has 128 divisors (see below), whose sum is σ = 1083607200. Its totient is φ = 156672000.

The previous prime is 413743951. The next prime is 413744021. The reversal of 413744000 is 447314.

It is a tau number, because it is divible by the number of its divisors (128).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 303320 + ... + 304680.

Almost surely, 2^413744000 is an apocalyptic number.

413744000 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 413744000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (541803600).

413744000 is an abundant number, since it is smaller than the sum of its proper divisors (669863200).

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

413744000 is a wasteful number, since it uses less digits than its factorization.

413744000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1409 (or 1387 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 23.

The square root of 413744000 is about 20340.6981197795. The cubic root of 413744000 is about 745.1503382623.

The spelling of 413744000 in words is "four hundred thirteen million, seven hundred forty-four thousand".