417978448560 has 560 divisors, whose sum is σ = 1536347381760. Its totient is φ = 105548935680.

The previous prime is 417978448553. The next prime is 417978448583. The reversal of 417978448560 is 65844879714.

417978448560 is a `hidden beast` number, since 4 + 1 + 7 + 97 + 8 + 4 + 485 + 60 = 666.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 111 ways as a sum of consecutive naturals, for example, 84969781 + ... + 84974699.

Almost surely, 2^417978448560 is an apocalyptic number.

417978448560 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 417978448560, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (768173690880).

417978448560 is an abundant number, since it is smaller than the sum of its proper divisors (1118368933200).

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

417978448560 is a wasteful number, since it uses less digits than its factorization.

417978448560 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5028 (or 5007 counting only the distinct ones).

The product of its (nonzero) digits is 54190080, while the sum is 63.

The spelling of 417978448560 in words is "four hundred seventeen billion, nine hundred seventy-eight million, four hundred forty-eight thousand, five hundred sixty".