413674800 has 480 divisors, whose sum is σ = 1710795264. Its totient is φ = 83635200.

The previous prime is 413674771. The next prime is 413674831. The reversal of 413674800 is 8476314.

It is a super-2 number, since 2×413674800² = 342253680310080000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (33).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 11180382 + ... + 11180418.

Almost surely, 2^413674800 is an apocalyptic number.

413674800 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 413674800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (855397632).

413674800 is an abundant number, since it is smaller than the sum of its proper divisors (1297120464).

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

413674800 is a wasteful number, since it uses less digits than its factorization.

413674800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 65 counting only the distinct ones).

The product of its (nonzero) digits is 16128, while the sum is 33.

The square root of 413674800 is about 20338.9970254189. The cubic root of 413674800 is about 745.1087930246.

The spelling of 413674800 in words is "four hundred thirteen million, six hundred seventy-four thousand, eight hundred".