413053920 has 288 divisors, whose sum is σ = 1534740480. Its totient is φ = 100776960.

The previous prime is 413053909. The next prime is 413053957. The reversal of 413053920 is 29350314.

It is a tau number, because it is divible by the number of its divisors (288).

It is a super-2 number, since 2×413053920² = 341227081654732800, which contains 22 as substring.

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, 847917 + ... + 848403.

It is an arithmetic number, because the mean of its divisors is an integer number (5328960).

Almost surely, 2^413053920 is an apocalyptic number.

413053920 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 413053920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (767370240).

413053920 is an abundant number, since it is smaller than the sum of its proper divisors (1121686560).

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

413053920 is a wasteful number, since it uses less digits than its factorization.

413053920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 558 (or 547 counting only the distinct ones).

The product of its (nonzero) digits is 3240, while the sum is 27.

The square root of 413053920 is about 20323.7280044779. The cubic root of 413053920 is about 744.7358311479.

The spelling of 413053920 in words is "four hundred thirteen million, fifty-three thousand, nine hundred twenty".