463689072 has 480 divisors, whose sum is σ = 1782743040. Its totient is φ = 108864000.

The previous prime is 463689011. The next prime is 463689073. The reversal of 463689072 is 270986364.

463689072 is a `hidden beast` number, since 4 + 636 + 8 + 9 + 0 + 7 + 2 = 666.

It is a Smith number, since the sum of its digits (45) coincides with the sum of the digits of its prime factors.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (463689073) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 6530797 + ... + 6530867.

It is an arithmetic number, because the mean of its divisors is an integer number (3714048).

Almost surely, 2^463689072 is an apocalyptic number.

463689072 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 463689072, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (891371520).

463689072 is an abundant number, since it is smaller than the sum of its proper divisors (1319053968).

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

463689072 is a wasteful number, since it uses less digits than its factorization.

463689072 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 153 (or 144 counting only the distinct ones).

The product of its (nonzero) digits is 435456, while the sum is 45.

The square root of 463689072 is about 21533.4407840456. The cubic root of 463689072 is about 774.0023636328.

The spelling of 463689072 in words is "four hundred sixty-three million, six hundred eighty-nine thousand, seventy-two".