417 has 4 divisors (see below), whose sum is σ = 560. Its totient is φ = 276.

The previous prime is 409. The next prime is 419. The reversal of 417 is 714.

417 is nontrivially palindromic in base 16.

It is a semiprime because it is the product of two primes, and also a Blum integer, because the two primes are equal to 3 mod 4.

It is not a de Polignac number, because 417 - 2³ = 409 is a prime.

It is a D-number.

It is a Duffinian number.

417 is an undulating number in base 16.

It is a plaindrome in base 7, base 11 and base 15.

It is a nialpdrome in base 8.

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 3 ways as a sum of consecutive naturals, for example, 67 + ... + 72.

It is an arithmetic number, because the mean of its divisors is an integer number (140).

It is a Proth number, since it is equal to 13 ⋅ 2⁵ + 1 and 13 < 2⁵.

It is an amenable number.

417 is a deficient number, since it is larger than the sum of its proper divisors (143).

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

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

The sum of its prime factors is 142.

The product of its digits is 28, while the sum is 12.

The square root of 417 is about 20.4205778567. The cubic root of 417 is about 7.4709991155.

It can be divided in two parts, 4 and 17, that added together give a triangular number (21 = T₆).

The spelling of 417 in words is "four hundred seventeen", and thus it is an aban number and an iban number.