414 has 12 divisors (see below), whose sum is σ = 936.
Its totient is φ = 132.
The previous prime is 409. The next prime is 419.
414 is nontrivially palindromic in base 8 and base 10.
It is an interprime number because it is at equal distance from previous prime (409) and next prime (419).
It is a Harshad number since it is a multiple of its sum of digits (9).
It is an Ulam number.
It is an alternating number because its digits alternate between even and odd.
414 is an undulating number in base 8 and base 10.
It is a Curzon number.
It is a plaindrome in base 11, base 13 and base 16.
It is a nialpdrome in base 9.
It is a junction number, because it is equal to n+sod(n) for n = 396 and 405.
It is a congruent number.
It is not an unprimeable number, because it can be changed into a prime (419) by changing a digit.
It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 7 + ... + 29.
It is an arithmetic number, because the mean of its divisors is an integer number (78).
It is a practical number, because each smaller number is the sum of distinct divisors of 414, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (468).
414 is an abundant number, since it is smaller than the sum of its proper divisors (522).
It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.
414 is a wasteful number, since it uses less digits than its factorization.
414 is an evil number, because the sum of its binary digits is even.
The sum of its prime factors is 31 (or 28 counting only the distinct ones).
The product of its digits is 16, while the sum is 9.
The square root of 414 is about 20.3469899494.
The cubic root of 414 is about 7.4530399137.
The spelling of 414 in words is "four hundred fourteen", and is thus an aban number and an iban number.