413 has 4 divisors (see below), whose sum is σ = 480. Its totient is φ = 348.

The previous prime is 409. The next prime is 419. The reversal of 413 is 314.

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, and also an emirpimes, since its reverse is a distinct semiprime: 314 = 2 ⋅157.

It is a cyclic number.

It is not a de Polignac number, because 413 - 2² = 409 is a prime.

It is a Duffinian number.

It is a Curzon number.

It is a plaindrome in base 11, base 13 and base 16.

It is a self number, because there is not a number n which added to its sum of digits gives 413.

It is a congruent number.

It is a panconsummate 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 3 ways as a sum of consecutive naturals, for example, 23 + ... + 36.

It is an arithmetic number, because the mean of its divisors is an integer number (120).

It is an amenable number.

413 is a deficient number, since it is larger than the sum of its proper divisors (67).

413 is an equidigital number, since it uses as much as digits as its factorization.

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

The sum of its prime factors is 66.

The product of its digits is 12, while the sum is 8.

The square root of 413 is about 20.3224014329. The cubic root of 413 is about 7.4470342383.

Adding to 413 its reverse (314), we get a palindrome (727).

Subtracting from 413 its reverse (314), we obtain a palindrome (99).

It can be divided in two parts, 41 and 3, that added together give a palindrome (44).

The spelling of 413 in words is "four hundred thirteen", and thus it is an aban number.