8414 has 8 divisors (see below), whose sum is σ = 14448. Its totient is φ = 3600.

The previous prime is 8389. The next prime is 8419. The reversal of 8414 is 4148.

It is a happy number.

8414 is nontrivially palindromic in base 13.

8414 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is a sphenic number, since it is the product of 3 distinct primes.

It is a Curzon number.

It is a plaindrome in base 9.

It is a junction number, because it is equal to n+sod(n) for n = 8392 and 8401.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (8419) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 287 + ... + 314.

It is an arithmetic number, because the mean of its divisors is an integer number (1806).

2⁸⁴¹⁴ is an apocalyptic number.

8414 is a deficient number, since it is larger than the sum of its proper divisors (6034).

8414 is a wasteful number, since it uses less digits than its factorization.

8414 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 610.

The product of its digits is 128, while the sum is 17.

The square root of 8414 is about 91.7278583637. The cubic root of 8414 is about 20.3392141609.

It can be divided in two parts, 841 and 4, that multiplied together give a square (3364 = 58²).

The spelling of 8414 in words is "eight thousand, four hundred fourteen".