415464000 has 224 divisors, whose sum is σ = 1568476416. Its totient is φ = 94924800.

The previous prime is 415463999. The next prime is 415464031. The reversal of 415464000 is 464514.

It is a tau number, because it is divible by the number of its divisors (224).

It is a super-2 number, since 2×415464000² = 345220670592000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 166764 + ... + 169236.

Almost surely, 2^415464000 is an apocalyptic number.

415464000 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 415464000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (784238208).

415464000 is an abundant number, since it is smaller than the sum of its proper divisors (1153012416).

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

415464000 is a wasteful number, since it uses less digits than its factorization.

415464000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2510 (or 2490 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 24.

The square root of 415464000 is about 20382.9340380623. The cubic root of 415464000 is about 746.1814804277.

The spelling of 415464000 in words is "four hundred fifteen million, four hundred sixty-four thousand".