415 has 4 divisors (see below), whose sum is σ = 504. Its totient is φ = 328.

The previous prime is 409. The next prime is 419. The reversal of 415 is 514.

415 = 7^{2} + 8^{2} + ... + 11^{2}.

It is a semiprime because it is the product of two primes, and also an emirpimes, since its reverse is a distinct semiprime: 514 = 2 ⋅257.

It is a cyclic number.

It is not a de Polignac number, because 415 - 2^{5} = 383 is a prime.

It is a Duffinian number.

415 is a lucky number.

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

It is a nialpdrome in base 9.

It is a zygodrome in base 2.

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 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, 37 + ... + 46.

It is an arithmetic number, because the mean of its divisors is an integer number (126).

415 is a deficient number, since it is larger than the sum of its proper divisors (89).

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

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

The sum of its prime factors is 88.

The product of its digits is 20, while the sum is 10.

The square root of 415 is about 20.3715487875. The cubic root of 415 is about 7.4590359259.

Adding to 415 its product of digits (20), we get a triangular number (435 = T_{29}).

Adding to 415 its reverse (514), we get a palindrome (929).

Subtracting 415 from its reverse (514), we obtain a palindrome (99).

The spelling of 415 in words is "four hundred fifteen", and thus it is an aban number.

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