414208 has 20 divisors (see below), whose sum is σ = 828630. Its totient is φ = 206848.

The previous prime is 414203. The next prime is 414209. The reversal of 414208 is 802414.

It can be written as a sum of positive squares in only one way, i.e., 278784 + 135424 = 528^2 + 368^2 .

It is a hoax number, since the sum of its digits (19) coincides with the sum of the digits of its distinct prime factors.

It is a nialpdrome in base 16.

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

414208 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 108 + ... + 916.

2⁴¹⁴²⁰⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 414208, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (414315).

414208 is a primitive abundant number, since it is smaller than the sum of its proper divisors, none of which is abundant.

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

414208 is an frugal number, since it uses more digits than its factorization.

414208 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 827 (or 811 counting only the distinct ones).

The product of its (nonzero) digits is 256, while the sum is 19.

The square root of 414208 is about 643.5899315558. The cubic root of 414208 is about 74.5428787890.

The spelling of 414208 in words is "four hundred fourteen thousand, two hundred eight".