415968000 has 288 divisors, whose sum is σ = 1581565440. Its totient is φ = 94924800.

The previous prime is 415967987. The next prime is 415968017. The reversal of 415968000 is 869514.

It is a hoax number, since the sum of its digits (33) coincides with the sum of the digits of its distinct prime factors.

It is a congruent number.

It is an unprimeable number.

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 31 ways as a sum of consecutive naturals, for example, 671691 + ... + 672309.

Almost surely, 2^415968000 is an apocalyptic number.

415968000 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 415968000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (790782720).

415968000 is an abundant number, since it is smaller than the sum of its proper divisors (1165597440).

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

415968000 is an equidigital number, since it uses as much as digits as its factorization.

415968000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 660 (or 636 counting only the distinct ones).

The product of its (nonzero) digits is 8640, while the sum is 33.

The square root of 415968000 is about 20395.2935747441. The cubic root of 415968000 is about 746.4830897898.

The spelling of 415968000 in words is "four hundred fifteen million, nine hundred sixty-eight thousand".