414764064 has 288 divisors, whose sum is σ = 1440863424. Its totient is φ = 115706880.

The previous prime is 414764033. The next prime is 414764069. The reversal of 414764064 is 460467414.

414764064 is a `hidden beast` number, since 4 + 1 + 4 + 7 + 640 + 6 + 4 = 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 (36).

It is not an unprimeable number, because it can be changed into a prime (414764069) by changing a digit.

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 47 ways as a sum of consecutive naturals, for example, 1111782 + ... + 1112154.

It is an arithmetic number, because the mean of its divisors is an integer number (5002998).

Almost surely, 2^414764064 is an apocalyptic number.

414764064 is a gapful number since it is divisible by the number (44) 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 414764064, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (720431712).

414764064 is an abundant number, since it is smaller than the sum of its proper divisors (1026099360).

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

414764064 is a wasteful number, since it uses less digits than its factorization.

414764064 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 422 (or 402 counting only the distinct ones).

The product of its (nonzero) digits is 64512, while the sum is 36.

The square root of 414764064 is about 20365.7571428120. The cubic root of 414764064 is about 745.7622119699.

The spelling of 414764064 in words is "four hundred fourteen million, seven hundred sixty-four thousand, sixty-four".