412848000 has 384 divisors, whose sum is σ = 1539008640. Its totient is φ = 105984000.

The previous prime is 412847971. The next prime is 412848011. The reversal of 412848000 is 848214.

It is a tau number, because it is divible by the number of its divisors (384).

It is a super-2 number, since 2×412848000² = 340886942208000000, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 6767970 + ... + 6768030.

It is an arithmetic number, because the mean of its divisors is an integer number (4007835).

Almost surely, 2^412848000 is an apocalyptic number.

412848000 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 412848000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (769504320).

412848000 is an abundant number, since it is smaller than the sum of its proper divisors (1126160640).

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

412848000 is a wasteful number, since it uses less digits than its factorization.

412848000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 143 (or 118 counting only the distinct ones).

The product of its (nonzero) digits is 2048, while the sum is 27.

The square root of 412848000 is about 20318.6613732303. The cubic root of 412848000 is about 744.6120527207.

It can be divided in two parts, 41284 and 8000, that added together give a square (49284 = 222²).

The spelling of 412848000 in words is "four hundred twelve million, eight hundred forty-eight thousand".