417424784216400 has 480 divisors, whose sum is σ = 1492597907600000. Its totient is φ = 110798449827840.

The previous prime is 417424784216359. The next prime is 417424784216431. The reversal of 417424784216400 is 4612487424714.

417424784216400 is a `hidden beast` number, since 4 + 1 + 7 + 4 + 2 + 478 + 4 + 2 + 164 + 0 + 0 = 666.

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

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, 10567963851 + ... + 10568003349.

Almost surely, 2^{417424784216400} is an apocalyptic number.

417424784216400 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 417424784216400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (746298953800000).

417424784216400 is an abundant number, since it is smaller than the sum of its proper divisors (1075173123383600).

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

417424784216400 is a wasteful number, since it uses less digits than its factorization.

417424784216400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 44028 (or 44011 counting only the distinct ones).

The product of its (nonzero) digits is 9633792, while the sum is 54.

The spelling of 417424784216400 in words is "four hundred seventeen trillion, four hundred twenty-four billion, seven hundred eighty-four million, two hundred sixteen thousand, four hundred".