416973312 has 320 divisors, whose sum is σ = 1466572800. Its totient is φ = 114462720.

The previous prime is 416973251. The next prime is 416973341. The reversal of 416973312 is 213379614.

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

It is a nude number because it is divisible by every one of its digits.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 2999739 + ... + 2999877.

It is an arithmetic number, because the mean of its divisors is an integer number (4583040).

Almost surely, 2^416973312 is an apocalyptic number.

416973312 is a gapful number since it is divisible by the number (42) 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 416973312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (733286400).

416973312 is an abundant number, since it is smaller than the sum of its proper divisors (1049599488).

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

416973312 is a wasteful number, since it uses less digits than its factorization.

416973312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 204 (or 182 counting only the distinct ones).

The product of its digits is 27216, while the sum is 36.

The square root of 416973312 is about 20419.9243877151. The cubic root of 416973312 is about 747.0839730763.

The spelling of 416973312 in words is "four hundred sixteen million, nine hundred seventy-three thousand, three hundred twelve".