416000000 has 168 divisors, whose sum is σ = 1119712230. Its totient is φ = 153600000.

The previous prime is 415999967. The next prime is 416000027. The reversal of 416000000 is 614.

It can be written as a sum of positive squares in 7 ways, for example, as 299705344 + 116294656 = 17312^2 + 10784^2 .

It is a hoax number, since the sum of its digits (11) coincides with the sum of the digits of its distinct prime factors.

It is an unprimeable number.

It is a polite number, since it can be written in 13 ways as a sum of consecutive naturals, for example, 31999994 + ... + 32000006.

Almost surely, 2^416000000 is an apocalyptic number.

416000000 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 416000000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (559856115).

416000000 is an abundant number, since it is smaller than the sum of its proper divisors (703712230).

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

416000000 is an frugal number, since it uses more digits than its factorization.

416000000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 65 (or 20 counting only the distinct ones).

The product of its (nonzero) digits is 24, while the sum is 11.

The square root of 416000000 is about 20396.0780543711. The cubic root of 416000000 is about 746.5022313634.

Adding to 416000000 its reverse (614), we get a palindrome (416000614).

It can be divided in two parts, 4 and 16000000, that multiplied together give a 6-th power (64000000 = 20⁶).

The spelling of 416000000 in words is "four hundred sixteen million", and thus it is an aban number.