413772000 has 288 divisors, whose sum is σ = 1438111584. Its totient is φ = 103936000.

The previous prime is 413771989. The next prime is 413772013. The reversal of 413772000 is 277314.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 10091980 + ... + 10092020.

It is an arithmetic number, because the mean of its divisors is an integer number (4993443).

Almost surely, 2^413772000 is an apocalyptic number.

413772000 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 413772000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (719055792).

413772000 is an abundant number, since it is smaller than the sum of its proper divisors (1024339584).

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

413772000 is a wasteful number, since it uses less digits than its factorization.

413772000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 127 (or 80 counting only the distinct ones).

The product of its (nonzero) digits is 1176, while the sum is 24.

The square root of 413772000 is about 20341.3863834302. The cubic root of 413772000 is about 745.1671471576.

The spelling of 413772000 in words is "four hundred thirteen million, seven hundred seventy-two thousand".