414201200 has 120 divisors (see below), whose sum is σ = 1176725280. Its totient is φ = 137088000.

The previous prime is 414201133. The next prime is 414201211. The reversal of 414201200 is 2102414.

It is a Harshad number since it is a multiple of its sum of digits (14).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 78650 + ... + 83750.

It is an arithmetic number, because the mean of its divisors is an integer number (9806044).

Almost surely, 2^414201200 is an apocalyptic number.

414201200 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 414201200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (588362640).

414201200 is an abundant number, since it is smaller than the sum of its proper divisors (762524080).

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

414201200 is a wasteful number, since it uses less digits than its factorization.

414201200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 5155 (or 5144 counting only the distinct ones).

The product of its (nonzero) digits is 64, while the sum is 14.

The square root of 414201200 is about 20351.9335690740. The cubic root of 414201200 is about 745.4247086646.

Adding to 414201200 its reverse (2102414), we get a palindrome (416303614).

The spelling of 414201200 in words is "four hundred fourteen million, two hundred one thousand, two hundred".