419904000000 has 819 divisors, whose sum is σ = 1574347641061. Its totient is φ = 111974400000.

The previous prime is 419903999989. The next prime is 419904000007. The reversal of 419904000000 is 409914.

The square root of 419904000000 is 648000.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 3 ways, for example, as 367876214784 + 52027785216 = 606528^2 + 228096^2 .

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (419904000007) by changing a digit.

It is a polite number, since it can be written in 62 ways as a sum of consecutive naturals, for example, 83980799998 + ... + 83980800002.

Almost surely, 2^419904000000 is an apocalyptic number.

419904000000 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

419904000000 is the 648000-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 419904000000

419904000000 is an abundant number, since it is smaller than the sum of its proper divisors (1154443641061).

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

419904000000 is an frugal number, since it uses more digits than its factorization.

419904000000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 78 (or 10 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

Multiplying 419904000000 by its product of nonzero digits (1296), we get a square (544195584000000 = 23328000²).

419904000000 divided by its product of nonzero digits (1296) gives a square (324000000 = 18000²).

Adding to 419904000000 its reverse (409914), we get a palindrome (419904409914).

The spelling of 419904000000 in words is "four hundred nineteen billion, nine hundred four million", and thus it is an aban number.