412776000 has 840 divisors, whose sum is σ = 1913007096. Its totient is φ = 87091200.

The previous prime is 412775999. The next prime is 412776011. The reversal of 412776000 is 677214.

It can be written as a sum of positive squares in 4 ways, for example, as 65028096 + 347747904 = 8064^2 + 18648^2 .

It is a tau number, because it is divible by the number of its divisors (840).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 31751994 + ... + 31752006.

Almost surely, 2^412776000 is an apocalyptic number.

412776000 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 412776000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (956503548).

412776000 is an abundant number, since it is smaller than the sum of its proper divisors (1500231096).

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

412776000 is a wasteful number, since it uses less digits than its factorization.

412776000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 66 (or 30 counting only the distinct ones).

The product of its (nonzero) digits is 2352, while the sum is 27.

The square root of 412776000 is about 20316.8895257123. The cubic root of 412776000 is about 744.5687638390.

The spelling of 412776000 in words is "four hundred twelve million, seven hundred seventy-six thousand".