414200 has 48 divisors (see below), whose sum is σ = 1023000. Its totient is φ = 155520.

The previous prime is 414199. The next prime is 414203. The reversal of 414200 is 2414.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 414200.

It is not an unprimeable number, because it can be changed into a prime (414203) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 3746 + ... + 3854.

2⁴¹⁴²⁰⁰ is an apocalyptic number.

414200 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 414200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (511500).

414200 is an abundant number, since it is smaller than the sum of its proper divisors (608800).

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

414200 is a wasteful number, since it uses less digits than its factorization.

414200 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 144 (or 135 counting only the distinct ones).

The product of its (nonzero) digits is 32, while the sum is 11.

The square root of 414200 is about 643.5837163882. The cubic root of 414200 is about 74.5423988797.

Adding to 414200 its reverse (2414), we get a palindrome (416614).

The spelling of 414200 in words is "four hundred fourteen thousand, two hundred", and thus it is an iban number.