413972400 has 240 divisors, whose sum is σ = 1414838016. Its totient is φ = 103234560.

The previous prime is 413972393. The next prime is 413972401. The reversal of 413972400 is 4279314.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (240).

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413972401) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 1462659 + ... + 1462941.

Almost surely, 2^413972400 is an apocalyptic number.

413972400 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 413972400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (707419008).

413972400 is an abundant number, since it is smaller than the sum of its proper divisors (1000865616).

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

413972400 is a wasteful number, since it uses less digits than its factorization.

413972400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 380 (or 369 counting only the distinct ones).

The product of its (nonzero) digits is 6048, while the sum is 30.

The square root of 413972400 is about 20346.3117050732. The cubic root of 413972400 is about 745.2874286931.

The spelling of 413972400 in words is "four hundred thirteen million, nine hundred seventy-two thousand, four hundred".