414420403200 has 264 divisors, whose sum is σ = 1429238457408. Its totient is φ = 105706782720.

The previous prime is 414420403171. The next prime is 414420403207. The reversal of 414420403200 is 2304024414.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is not an unprimeable number, because it can be changed into a prime (414420403207) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1649094 + ... + 1883706.

Almost surely, 2^414420403200 is an apocalyptic number.

414420403200 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 414420403200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (714619228704).

414420403200 is an abundant number, since it is smaller than the sum of its proper divisors (1014818054208).

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

414420403200 is a wasteful number, since it uses less digits than its factorization.

414420403200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 234669 (or 234646 counting only the distinct ones).

The product of its (nonzero) digits is 3072, while the sum is 24.

Adding to 414420403200 its reverse (2304024414), we get a palindrome (416724427614).

The spelling of 414420403200 in words is "four hundred fourteen billion, four hundred twenty million, four hundred three thousand, two hundred".