415776000 has 288 divisors, whose sum is σ = 1423408896. Its totient is φ = 107520000.

The previous prime is 415775977. The next prime is 415776001. The reversal of 415776000 is 677514.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (415776001) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 5855965 + ... + 5856035.

It is an arithmetic number, because the mean of its divisors is an integer number (4942392).

Almost surely, 2^415776000 is an apocalyptic number.

415776000 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 415776000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (711704448).

415776000 is an abundant number, since it is smaller than the sum of its proper divisors (1007632896).

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

415776000 is an equidigital number, since it uses as much as digits as its factorization.

415776000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 166 (or 142 counting only the distinct ones).

The product of its (nonzero) digits is 5880, while the sum is 30.

The square root of 415776000 is about 20390.5860631812. The cubic root of 415776000 is about 746.3682197272.

The spelling of 415776000 in words is "four hundred fifteen million, seven hundred seventy-six thousand".