414250320400 has 240 divisors, whose sum is σ = 1146616611840. Its totient is φ = 140883724800.

The previous prime is 414250320373. The next prime is 414250320409. The reversal of 414250320400 is 4023052414.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (25).

It is not an unprimeable number, because it can be changed into a prime (414250320409) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 274155645 + ... + 274157155.

It is an arithmetic number, because the mean of its divisors is an integer number (4777569216).

Almost surely, 2^414250320400 is an apocalyptic number.

414250320400 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 414250320400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (573308305920).

414250320400 is an abundant number, since it is smaller than the sum of its proper divisors (732366291440).

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

414250320400 is a wasteful number, since it uses less digits than its factorization.

414250320400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2262 (or 2251 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 25.

Adding to 414250320400 its reverse (4023052414), we get a palindrome (418273372814).

The spelling of 414250320400 in words is "four hundred fourteen billion, two hundred fifty million, three hundred twenty thousand, four hundred".