40419064800 has 864 divisors, whose sum is σ = 161059691520. Its totient is φ = 9853747200.

The previous prime is 40419064753. The next prime is 40419064843. The reversal of 40419064800 is 846091404.

It is a happy number.

40419064800 is a `hidden beast` number, since 4 + 0 + 4 + 1 + 9 + 0 + 648 + 0 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (864).

It is a super-3 number, since 3×40419064800³ (a number of 33 digits) contains 333 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 114501424 + ... + 114501776.

It is an arithmetic number, because the mean of its divisors is an integer number (186411680).

Almost surely, 2^40419064800 is an apocalyptic number.

40419064800 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 40419064800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (80529845760).

40419064800 is an abundant number, since it is smaller than the sum of its proper divisors (120640626720).

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

40419064800 is a wasteful number, since it uses less digits than its factorization.

40419064800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 438 (or 413 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The spelling of 40419064800 in words is "forty billion, four hundred nineteen million, sixty-four thousand, eight hundred".