408 has 16 divisors (see below), whose sum is σ = 1080. Its totient is φ = 128.

The previous prime is 401. The next prime is 409. The reversal of 408 is 804.

408 is nontrivially palindromic in base 5 and base 14.

408 is an esthetic number in base 14, because in such base its adjacent digits differ by 1.

It is a Harshad number since it is a multiple of its sum of digits (12).

It is a super Niven number, because it is divisible the sum of any subset of its (nonzero) digits.

408 is an idoneal number.

408 is an undulating number in base 14.

It is a plaindrome in base 7 and base 13.

It is a nialpdrome in base 8.

It is a zygodrome in base 2 and base 7.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 393 and 402.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (401) by changing a digit.

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

In principle, a polygon with 408 sides can be constructed with ruler and compass.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 16 + ... + 32.

408 is the 12-th octagonal number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 408, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (540).

408 is an abundant number, since it is smaller than the sum of its proper divisors (672).

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

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

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

The sum of its prime factors is 26 (or 22 counting only the distinct ones).

The product of its (nonzero) digits is 32, while the sum is 12.

The square root of 408 is about 20.1990098767. The cubic root of 408 is about 7.4168595385.

The spelling of 408 in words is "four hundred eight", and thus it is an aban number.

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