416606976000 has 1152 divisors, whose sum is σ = 1608180799680. Its totient is φ = 107495424000.

The previous prime is 416606975987. The next prime is 416606976013. The reversal of 416606976000 is 679606614.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (416606975987) and next prime (416606976013).

It is a tau number, because it is divible by the number of its divisors (1152).

It is a super-2 number, since 2×416606976000² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 2301695910 + ... + 2301696090.

Almost surely, 2^416606976000 is an apocalyptic number.

416606976000 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 416606976000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (804090399840).

416606976000 is an abundant number, since it is smaller than the sum of its proper divisors (1191573823680).

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

416606976000 is an equidigital number, since it uses as much as digits as its factorization.

416606976000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 270 (or 228 counting only the distinct ones).

The product of its (nonzero) digits is 326592, while the sum is 45.

The spelling of 416606976000 in words is "four hundred sixteen billion, six hundred six million, nine hundred seventy-six thousand".