416267509432320 has 3840 divisors, whose sum is σ = 1895972849971200. Its totient is φ = 85271676715008.

The previous prime is 416267509432319. The next prime is 416267509432351. The reversal of 416267509432320 is 23234905762614.

416267509432320 is a `hidden beast` number, since 4 + 1 + 6 + 2 + 67 + 509 + 43 + 2 + 32 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (3840).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 2492619816877 + ... + 2492619817043.

It is an arithmetic number, because the mean of its divisors is an integer number (493742929680).

Almost surely, 2^{416267509432320} is an apocalyptic number.

416267509432320 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 416267509432320, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (947986424985600).

416267509432320 is an abundant number, since it is smaller than the sum of its proper divisors (1479705340538880).

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

416267509432320 is an frugal number, since it uses more digits than its factorization.

416267509432320 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 288 (or 240 counting only the distinct ones).

The product of its (nonzero) digits is 13063680, while the sum is 54.

The spelling of 416267509432320 in words is "four hundred sixteen trillion, two hundred sixty-seven billion, five hundred nine million, four hundred thirty-two thousand, three hundred twenty".