413683200 has 720 divisors, whose sum is σ = 1846965120. Its totient is φ = 89579520.

The previous prime is 413683183. The next prime is 413683261. The reversal of 413683200 is 2386314.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×413683200² = 342267579924480000, which contains 22 as substring.

It is a hoax number, since the sum of its digits (27) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a nialpdrome in base 12.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 21772791 + ... + 21772809.

Almost surely, 2^413683200 is an apocalyptic number.

413683200 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 413683200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (923482560).

413683200 is an abundant number, since it is smaller than the sum of its proper divisors (1433281920).

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

413683200 is an equidigital number, since it uses as much as digits as its factorization.

413683200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 69 (or 36 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 27.

The square root of 413683200 is about 20339.2035242288. The cubic root of 413683200 is about 745.1138363352.

The spelling of 413683200 in words is "four hundred thirteen million, six hundred eighty-three thousand, two hundred".