414097776000 has 768 divisors, whose sum is σ = 1526597280000. Its totient is φ = 107539660800.

The previous prime is 414097775947. The next prime is 414097776041. The reversal of 414097776000 is 677790414.

It is a super-3 number, since 3×414097776000³ (a number of 36 digits) contains 333 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, 1012463796 + ... + 1012464204.

It is an arithmetic number, because the mean of its divisors is an integer number (1987756875).

Almost surely, 2^414097776000 is an apocalyptic number.

414097776000 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 414097776000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (763298640000).

414097776000 is an abundant number, since it is smaller than the sum of its proper divisors (1112499504000).

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

414097776000 is a wasteful number, since it uses less digits than its factorization.

414097776000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 612 (or 587 counting only the distinct ones).

The product of its (nonzero) digits is 296352, while the sum is 45.

The spelling of 414097776000 in words is "four hundred fourteen billion, ninety-seven million, seven hundred seventy-six thousand".