413784900 has 108 divisors (see below), whose sum is σ = 1338914304. Its totient is φ = 106776000.

The previous prime is 413784871. The next prime is 413784937. The reversal of 413784900 is 9487314.

It is a happy number.

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 35 ways as a sum of consecutive naturals, for example, 20485 + ... + 35315.

Almost surely, 2^413784900 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413784900, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (669457152).

413784900 is an abundant number, since it is smaller than the sum of its proper divisors (925129404).

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

413784900 is a wasteful number, since it uses less digits than its factorization.

413784900 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 14882 (or 14872 counting only the distinct ones).

The product of its (nonzero) digits is 24192, while the sum is 36.

The square root of 413784900 is about 20341.7034684905. The cubic root of 413784900 is about 745.1748910007.

The spelling of 413784900 in words is "four hundred thirteen million, seven hundred eighty-four thousand, nine hundred".