414264195072 has 1152 divisors, whose sum is σ = 1620833760000. Its totient is φ = 103338934272.

The previous prime is 414264195049. The next prime is 414264195073. The reversal of 414264195072 is 270591462414.

414264195072 is a `hidden beast` number, since 41 + 42 + 64 + 1 + 9 + 507 + 2 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a super-2 number, since 2×414264195072² (a number of 24 digits) contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (414264195073) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 669247179 + ... + 669247797.

It is an arithmetic number, because the mean of its divisors is an integer number (1406973750).

Almost surely, 2^414264195072 is an apocalyptic number.

414264195072 is a gapful number since it is divisible by the number (42) 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 414264195072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (810416880000).

414264195072 is an abundant number, since it is smaller than the sum of its proper divisors (1206569564928).

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

414264195072 is a wasteful number, since it uses less digits than its factorization.

414264195072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 696 (or 663 counting only the distinct ones).

The product of its (nonzero) digits is 483840, while the sum is 45.

The spelling of 414264195072 in words is "four hundred fourteen billion, two hundred sixty-four million, one hundred ninety-five thousand, seventy-two".