414406056960 has 1408 divisors, whose sum is σ = 1809922682880. Its totient is φ = 88862883840.

The previous prime is 414406056947. The next prime is 414406056983. The reversal of 414406056960 is 69650604414.

It is a happy number.

414406056960 is a `hidden beast` number, since 41 + 4 + 40 + 6 + 0 + 569 + 6 + 0 = 666.

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 127 ways as a sum of consecutive naturals, for example, 1332495205 + ... + 1332495515.

Almost surely, 2^414406056960 is an apocalyptic number.

414406056960 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 414406056960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (904961341440).

414406056960 is an abundant number, since it is smaller than the sum of its proper divisors (1395516625920).

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

414406056960 is an equidigital number, since it uses as much as digits as its factorization.

414406056960 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 381 (or 345 counting only the distinct ones).

The product of its (nonzero) digits is 622080, while the sum is 45.

The spelling of 414406056960 in words is "four hundred fourteen billion, four hundred six million, fifty-six thousand, nine hundred sixty".