414252000 has 288 divisors, whose sum is σ = 1514769984. Its totient is φ = 107136000.

The previous prime is 414251989. The next prime is 414252001. The reversal of 414252000 is 252414.

414252000 is a `hidden beast` number, since 4 + 142 + 520 + 0 + 0 = 666.

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

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414252001) 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, 1331845 + ... + 1332155.

It is an arithmetic number, because the mean of its divisors is an integer number (5259618).

Almost surely, 2^414252000 is an apocalyptic number.

414252000 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 414252000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (757384992).

414252000 is an abundant number, since it is smaller than the sum of its proper divisors (1100517984).

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

414252000 is a wasteful number, since it uses less digits than its factorization.

414252000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 379 (or 358 counting only the distinct ones).

The product of its (nonzero) digits is 320, while the sum is 18.

The square root of 414252000 is about 20353.1815694746. The cubic root of 414252000 is about 745.4551817996.

The spelling of 414252000 in words is "four hundred fourteen million, two hundred fifty-two thousand".